SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

Report of Foreign Private Issuer

Pursuant to Rule 13a-16 or 15d-16 of the

Securities Exchange Act of 1934

For the month of June 2010

Commission File Number 1-13758

PORTUGAL TELECOM, SGPS, S.A.

(Exact name of registrant as specified in its charter)

Av. Fontes Pereira de Melo, 40

1069 - 300 Lisboa, Portugal

(Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F.

Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

Release  |  Lisbon  |  2 June 2010

Portugal Telecom informs on the proposal received from Telefónica

Following the announcement released on 1 June, the full proposal received from Telefónica is disclosed herein.

www.telecom.pt

To the attention of:

Mr. Henrique Granadeiro - Chairman of the Board of Directors of Portugal Telecom, SGPS S.A.

Mr. Zeinal Bava - Chief Executive Officer of Portugal Telecom, SGPS S.A.

The Board of Directors of Portugal Telecom, SGPS S.A.

Av. Fontes Pereira de Melo, 40

1069-300 Lisbon

June 1st, 2010

Dear Sirs,

Telefónica, S.A. (“Telefónica”) hereby submits to Portugal Telecom, SGPS, SA. (“Portugal Telecom”) a binding offer (the “Offer”) for the acquisition by Telefónica, directly or through any of its affiliates, of fifty percent (50%) of the shares of Brasilcel, N.V. (‘Brasilcel” or the “Company”) owned directly or indirectly by Portugal Telecom, in accordance with the terms and conditions set forth herein, through any of the Offer alternatives mentioned in this Offer (the “Transaction”).

This Offer shall constitute a binding commitment on our part subject to the terms provided below. Should you accept the Offer (in any of its alternatives), the terms and conditions herein will become legally binding.

1.     Alternative Offer Structures

1.1        Alternative A

Subject to the terms and conditions of this Offer, Telefónica proposes to acquire 50% of the total number of shares of the Company, owned directly or indirectly by Portugal Telecom, free and clear from any liens, charges, encumbrances and third party rights (the “Alternative A Shares”) for an aggregate purchase price of Euros 6,500 million (six thousand and five hundred million Euros) (the “Alternative A Consideration”). The Alternative A Consideration would be payable in cash, in immediately available funds on the date of completion of the acquisition of the Alternative A Shares (the “Closing A”).

1.2        Alternative B

Subject to the terms and conditions of this Offer, Telefónica alternatively proposes to acquire one third (1/3) of the 50% of the total number of shares of the Company, owned directly or indirectly by Portugal Telecom, free and clear from any liens, charges, encumbrances and third party rights (the “Alternative B Shares”) for an aggregate purchase price of 2,166,666,667 (two thousand one hundred and sixty six million six hundred and sixty six thousand and six hundred and sixty seven) Euros, equivalent to one third (1/3) of 6,500 (six thousand and five hundred) million Euros (the “Alternative B Consideration”). The Alternative B Consideration would be payable in cash, in immediately available funds on the date of completion of the acquisition of the Alternative B Shares (the “Closing B”).

Additionally, Telefónica would propose to offer to Portugal Telecom the right to put (the “Put”) all or part (and in such case the Put may be exercised in several times) of the two thirds (2/3) of the 50% of the total number of shares of the Company, owned directly or indirectly by Portugal Telecom after Closing B, free and clear from any liens, charges, encumbrances and third party rights (the “Alternative B Put Shares”) for an aggregate purchase price, for each relevant transfer, equivalent to (the “Alternative B Put Consideration”) an amount equal to 6,500 (six thousand and five hundred) million Euros multiplied by the percentage that the number of Alternative B Put Shares transferred from time to time represent over fifty percent (50%) of the total number of shares of the Company.

Telefónica undertakes to cause the Company to yearly pay dividends (or other type of distributions such reserves distributions, etc.) to its shareholders that permits that Portugal Telecom receives an amount equal to the Annual Amount until the earliest of (i) the date on which all the Alternative B Put Shares have been transferred by Portugal Telecom to Telefónica; and (ii) the third anniversary of the Closing B.

For this purpose, “Annual Amount” shall mean an amount that would result of applying a rate of five per cent (5%) over the purchase price attributable to the Alternative B Put Shares in each 12-month period starting on the date of the Closing B (or any anniversary thereof), provided, for the avoidance of doubt, that such amount shall not accrue interests starting on the date on which such amounts are paid by Telefónica to Portugal Telecom as a consequence of a transfer or Alternative B Put Shares. The Annual Amount shall be compounded on a yearly basis (assuming a year of 360 days) on each anniversary of the Closing B.

in the event that Telefónica fails to cause that the Company distributes dividends as provided in the previous paragraph, Telefónica and Portugal Telecom shall agree in good faith on other mechanism that allows Portugal Telecom to receive the aforesaid interest in an efficient manner.

If the dividends (or other distributions) paid by the Company exceed in any 12-month period starting on the Closing B the Annual Amount that would correspond to such period, the excess will be deducted from the Alternative B Put Consideration payable by Telefónica in the next transfer of Alternative B Put Shares.

The Put may be exercised by written notice delivered to Telefónica (the “put Exercise Notice”), one or more times, and at any time from the date of acceptance of this Offer until the third anniversary thereof, provided that each Put Exercise Notice shall comprise at least 10% of the total Alternative B Put Shares.

The Alternative B Put Consideration shall be payable in cash, in immediately available funds on the date of completion of the acquisition of the relevant portion of the Alternative B Put Shares.

1.3        Closing.

The consummation of any transfer of the shares shall occur as promptly as practicable but in no event later than 60 (sixty) days after (i) the date of acceptance of this Offer (in the event of the Closing A or the Closing B); or (ii) the delivery of the Put Exercise Notice (in the event of

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any transfer of all or a portion of Alternative B Put Shares); at the time and place as may be agreed upon by Portugal Telecom and Telefónica.

The Parties undertake to use their reasonable efforts to fulfil any requirements and to obtain any necessary approval necessary to effect either the Closing A or the Closing B, or any transfer of Alternative B Put Shares as soon as practicable and to enter into the documents required under Dutch Law for the valid transfer of shares.

1.4        Termination of Shareholders Agreement and Subscription Agreement.

On the date of the Closing A or the Closing B, as applicable, the Company’s Shareholders’ Agreement (as amended) and Subscription Agreement entered into by Portugal Telecom and Telefónica on October 17, 2002, shall terminate without any liability on either Portugal Telecom or Telefónica as a consequence of such termination.

1.5        Company’s Governance under Alternative B.

On the date on which the Closing B occurs:

(i)                           all the Supervisory Directors except for two (2) and all the Managing Directors appointed by Portugal Telecom, as well as the directors appointed following Portugal Telecom’s nomination in any of the Company’s subsidiaries, shall resign;

(ii)                        the replacing Directors will be appointed by nomination of Telefónica;

(iii)                     except for two Supervisory Directors to be appointed by Portugal Telecom, it shall withdraw any right to appoint Directors in any of the companies referred to in (i) above, including the Company; and

(iv)                    Portugal Telecom shall commit to vote its shares in the Company in accordance with the Telefónica’s instructions, including but not limited, in relation to corporate transactions involving the Company or any of its subsidiaries, including any corporate transaction with third parties, to the extent that such transactions are performed in accordance with fair valuations.

The right to appoint two Supervisory Directors out of twelvc (12) mentioned in (iii) above will expire on the date on which the interest of Portugal Telecom in the Company is reduced below ten percent (10%).

2.         Funding of the Transaction

Telefónica has available funds and credit lines to complete the Transaction and therefore this Offer is not subject to obtaining financing by Telefónica.

3.         No other conditions

This Offer is not subject to any other conditions. In particular:

(i)                           this Offer has been approved by the Board of Directors of Telefónica and thus this Offer is not subject to further approvals by Telefónica;

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(ii)                        this Offer is not subject to obtaining approvals from third parties in relation to the Transaction;

(iii)                     Telefónica would not require non-compete or non-solicitation commitments by Portugal Telecom;

(iv)                    Telefónica would not require to complete a due diligence process and therefore this Offer is not contingent on the outcome of such due diligence process.

4.         Limited representations and warranties

With respect to the Company, Telefónica does not require any representation or warranty other than customary representations and warranties in relation to authority to enter into the Transaction, ownership and good title over the Shares and absence of liens and encumbrances on the Shares.

5.         Vivo management / employees

Telefónica is pleased with the recent performance of Vivo and therefore it envisions the continuity of Vivo’s management, including contract with the CEO, which will be transferred to Vivo, and the preservation of Vivo employees’ rights.

6.         Subsequent tender offer

Telefónica contemplates to launch after Closing A or Closing B, as applicable, a tender offer over the voting shares (ON) of Vivo not owned by the Company. The purchase price offered in such tender offer would be 80% of the value attributed to each of the Vivo’s voting shares (ON) in this Offer.

7.         Portugal Telecom call on shares owned by Telefónica in Portugal Telecom.

Telefónica would propose to offer to Portugal Telecom the right to call, or to elect one or more third parties at its sole discretion to call (the “PT Call”) the shares held directly by Telefónica in Portugal Telecom (the “PT Call Shares”), representing approximately 8,5% of its share capital free and clear from any liens, charges, encumbrances and third party rights.

In the event of exercise by Portugal Telecom of the PT Call, Telefónica shall use its reasonable efforts to cause that an additional interest in Portugal Telecom of approximately 1,5% of its share capital, currently held by Telefónica’s direct or indirect subsidiaries, is also transferred to Portugal Telecom and, if Telefónica may effectively cause such transfer, “PT Call Shares” shall also comprise such additional shares.

The Call may be exercised by written notice delivered to Telefónica (the “Call Exercise Notice”) indicating the elected party or parties that will acquire the PT Call Shares, at the following dates:

(i)                           if Portugal Telecom elects to effect the Transaction following Alternative A, Portugal Telecom shall deliver the Call Exercise Notice on:

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a.               the date of Closing A, and in such event the purchase price of each PT Call Shares shall be equivalent to the volume weighted average price for Portugal Telecom shares on the Euronext Lisbon for the thirty (30) trading days immediately following the date on which the Board of Directors of Portugal Telecom accepts this Offer or calls the General Shareholders’ Meeting of Portugal Telecom to deliberate about the Offer; or

b.              the date that is two (2) months after the date of Closing A, and in such event the purchase price of each PT Call Shares shall be equivalent to the volume weighted average price for Portugal Telecom shares on the Euronext Lisbon for the sixty (60) days immediately prior to the date of delivery of the Call Exercise Notice; or

(ii)                        if Portugal Telecom elects to effect the Transaction following Alternative B:

a.               in relation to one third (1/3) of the PT Call Shares:

-                    the date of Closing B, and in such event the purchase price of each PT Call Shares shall be equivalent to the volume weighted average price for Portugal Telecom shares on the Euronext Lisbon for the thirty (30) trading days immediately following the date on which the Board of Directors of Portugal Telecom accepts this Offer or calls the General Shareholders’ Meeting of Portugal Telecom to deliberate about the Offer; or

-                    the date that is two (2) months after the date of Closing B, and in such event the purchase price of each PT Call Shares shall be equivalent to the volume weighted average price for Portugal Telecom shares on the Euronext Lisbon for the sixty (60) days immediately prior to the date of delivery of the Call Exercise Notice; and

b.              in relation to the remaining PT Call Shares, no later than on the date of the transfer of Alternative B Put Shares and for up to the same proportion of the portion of the Alternative B Put Shares being transferred, and in this event the purchase price of the PT Call Shares shall be equivalent to the volume weighted average price for Portugal Telecom shares on the Euronext Lisbon for the ninety (90) trading days immediately preceding the date of transfer of the relevant PT Call Shares, which average price shall be calculated based on the weighted average price of the shares for each day during such ninety (90) day trading period.

The consummation of any transfer of the relevant PT Call Shares shall occur as promptly as practicable but in any event no later than 60 (sixty) days after the delivery of the Call Exercise Notice at the time and place as may be agreed upon by Portugal Telecom and Telefónica.

For the avoidance of doubt, the PT Call shall be exercised in accordance with the periods mentioned in (i) and (ii) above, and in no event it may be exercise after the third anniversary of the date of acceptance of this Offer.

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From the date of the Closing A or the Closing B, as applicable, Telefónica undertakes to exercise its voting rights in relation to its direct interest in Portugal Telecom, in favour of the proposals submitted by the Board of Directors to the General Shareholders’ Meeting.

8.                            Dedic Acquisition by Telefónica.

Subject to the Closing A or the Closing B, as applicable, having occurred, Telefónica, directly or through any of its affiliates, will purchase from Portugal Telecom all but not part of the shares in Dedic, S.A. (the “Dedic Shares”) currently owned directly or indirectly by Portugal Telecom free and clear from any liens, charges, encumbrances and third party rights for a price resulting from an independent evaluation.

Immediately after the Closing A or the Closing B, as applicable, Portugal Telecom shall make available to Telefónica all necessary information to perform a customary due diligence process over Dedic (including tax, legal, financial, operational, commercial, labour and technical due diligence). Such due diligence process shall last thirty (30) Business Days after such information was made available. For the purposes of this Offer, “Business Day” shall mean a day other than a Saturday, Sunday or statutory holiday in Sao Paulo, Rio de Janeiro, Madrid, Lisbon or Amsterdam.

After finalization of the due diligence process, Portugal Telecom and Telefónica shall attempt to reach an agreement on the purchase price to be paid by Telefónica for the Dedic Shares. If Portugal Telecom and Telefónica are unable to reach an agreement on such purchase price within fifteen (15) Business Days after the finalization of the due diligence process, the Parties agree to start the independent evaluation procedure within a thirty days period from the date of acceptance of this Offer. The consummation of any transfer of the Dedic Shares shall occur as promptly as practicable and in any event no later than 30 (thirty) days after the delivery of the Dedic binding evaluation.

The independent evaluation will be undertaken by two leading international investment banks. For this purpose, each Party will appoint a bank from a list of three banks proposed by the other Party within 15 days following receipt of the list. Absence of appointment in such term will imply acceptance of any of the banks included in the list at the option of the Party that sent the list. The list of banks presented by each Party will exclude any bank which owns a significant direct or indirect interest in its share capital or has representation in the Board of the Party.

Should the two evaluations undertaken by the international investment banks referred to above, differ by more than five percentage points, a third evaluation shall be undertaken by another leading international investment bank, which will be appointed by mutual agreement of the Parties or, failing such agreement within 15 days following receipt of notice from one Party to the other seeking for agreement, by the appointed banks, and failing appointment by them, by the International Chamber of Commerce in Paris as Appointing Authority. The third bank must indicate a valuation within the values given by the two first investment banks and it will be binding for both Parties.

Should the two evaluations undertaken by the international investment banks referred to above differ by five percentage points or less, then the difference will be equally split between the Parties.

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Any valuation undertaken by a third leading international investment bank, as a result of any of the provisions above, will be binding upon the Parties hereto.

The investment banks appointed by Portugal Telecom and Telefónica, and the Third Investment Bank shall issue their valuation reports within 30 Business Days after their respective engagement, shall apply valuation criteria commonly used in relation to companies of the same sector as Dedic, according to market practice and shall take into account any findings of the due diligence process referred to above.

Portugal Telecom shall undertake to procure that, from the date of acceptance of this Offer and until the closing of the transfer of the Dedic Shares, Dedic shall be managed in the ordinary course of business in accordance with past practices.

9.                            Services.

9.1                       international Traffic.

Telefónica shall use its reasonable efforts in order to allow that, for the Service Period (as defined below), Vivo continues to execute existing agreements with Portugal Telecom or its’ affiliates regarding outgoing and incoming international and roaming both of voice and data.

9.2                       No material change in contracts with Sellers.

Telefónica shall use its reasonable efforts in order to avoid that, for a period of twelve (12) months from the date hereof, Vivo does not materially change the terms of any agreement between Vivo and any of the affiliates of Portugal Telecom or terminate or give notice to terminate any such agreements including but not limited to the agreements with Dedic, Sapo, PT Inovação, PT Comunicações and TMN; except in the event of any termination by cause.

9.3                       Formalisation of contracts with Sellers.

For a period of 12 (twelve) months for the date of acceptance of this Offer, Telefónica shall use its reasonable efforts to cause Vivo to formalise and execute any and all contracts with Portugal Telecom or any of its’ affiliates which (i) have been subject to preliminary agreement or understanding, or (ii) result from services provided by Portugal Telecom or any of its affiliates within the last 12 (twelve) months on an informal basis. For the avoidance of doubt, such agreements shall be formalised and executed an arm’s-length basis, observing under the terms and conditions resulting from the preliminary agreement or understanding or from the usual terms and conditions of the services provided, as applicable.

9.4                       Service Period

For the purposes of paragraph 9.1 above, “Service Period” shall mean:

(i)                           under Alternative A, the period of twelve (12) months following the Closing A;

(ii)                        under Alternative B, the shortest of:

-                    the period of twelve (12) months following the date on which Portugal Telecom has transferred to Telefónica ninety per cent of (90%) or more of 50% of the total

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number of shares of the Company, owned directly or indirectly by Portugal Telecom; and

-                    the period of thirty six (36) months following the date hereof.

10.       Effect of competition in Brazil

In the event that Portugal Telecom competes with Vivo in the wireline, wireless, or internet access businesses, either directly, either indirectly through any affiliate of Portugal Telecom (and for this purposes “affiliate” shall comprise any company in which Portugal Telecoms owns more than a 10% voting stake, any company under common control of PT and/or any company belonging to a group of any other company which owns a voting interest in Portugal Telecom of more than 10%):

(i)                                the provisions of paragraphs 9.1 to 9.4 above shall immediately terminate and in this event Vivo shall be free to terminate any agreement between Vivo and any of the affiliates of Portugal Telecom and to cease negotiations about future agreements, as referred in paragraphs 9.1 to 9.4 above;

(ii)                             any Supervisory Directors appointed by nomination of Portugal Telecom in the Company shall resign with immediate effect; and

(iii)                          Portugal Telecom shall immediately deliver a Put Exercise Notice and exercise the Put in relation to any Alternative B Put Shares not yet transferred by Portugal Telecom to Telefónica.

11.       Outstanding receivables

The following amounts shall be paid at the date of Closing A or Closing B, as the case may be:

(i)                           Telefónica shall cause Brasilcel to pay to Portugal Telecom an amount of Euros 52,860,000 (fifty two million, eight hundred and sixty thousand Euros), corresponding to the Portugal Telecom’s share in the Company’s portion of the declared and unpaid Vivo dividend of R$ 236.79 million, at the current exchange rate of 2.24R$/€, in respect of the 2009 net income; provided that such amount shall not be due by Telefónica in the event that such amount is distributed and paid to Portugal Telecom prior to the date of the Closing A or the Closing B, as applicable; and

(ii)                        Telefónica shall pay to Portugal Telecom (or Portugal Telecom to Telefónica depending if such amount is due by Telefónica or by Portugal Telecom) an amount to be agreed between Telefónica and Portugal Telecom corresponding to the net settlement of payments due by each party to the other, in relation to Vivo management fees, pending expenses and other costs.

12.       Non-compete

Each party shall refrain from  engaging or investing, directly or indirectly through any Affiliate, in any project in the telecommunication business (including fixed and mobile

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services, internet access and television services, but excluding any investment or activity currently held or performed as of the date hereof) that can be deemed to be in competition with the other within the Iberian market for a period starting on the date of Acceptance of the Offer until the latest of (i) 31st December 2011 or (ii) the date of consummation of the transfer of the last portion of Alternative B Put Shares.

13.       Validity of this Offer

This Offer will expire on June 30th, 2010, unless such term is extended by Telefónica in writing, or unless it is accepted in writing or rejected, by you on or before such date.

Telefónica is however prepared to grant an extension of the aforesaid validity period in the event that, given the relevance of this Offer, you decide to submit the same to the Portugal Telecom Shareholders’ Meeting.

14.       Termination of prior Offer

Provided that according to the release filed by Portugal Telecom with the Comissâo do Mercado de Valores Mobiliârios on May 10, 2010 on that date the Board of Directors of Portugal Telecom unanimously rejected the prior offer submitted by Telefónica on May 6, 2010, such prior offer shall be considered to be expired and shall cease to be effective.

15.       Structuring Flexibility

Upon acceptance of the Offer, Portugal Telecom undertakes to collaborate with Telefónica, including issuing favourable votes in this regard, in order to accommodate the most efficient Transaction structure, provided that they result in the same effects as the Offer.

16.       Confidentiality

This Offer is confidential for Portugal Telecom and shall not be disclosed by it, except in the event that Portugal Telecom is requested or required by law, regulation, or pursuant to any requirement of any supervisory authority, regulatory authority, stock exchange or other applicable judicial or governmental order to disclose the existence of this Offer or its terms and conditions. Should this be the case, Portugal Telecom will provide Telefónica with immediate notice thereof and Portugal Telecom will furnish, after written notification to Telefónica, only that portion of the information related to the Offer which is legally required to be disclosed and will exercise all reasonable efforts to obtain a protective order or other reliable assurance that confidential treatment will be accorded to the information related to the Offer.

17.       Governing law

This Offer shall in all respects, including as to validity, interpretation and effect, be governed by the laws of Portugal, and the courts of Lisbon shall have exclusive jurisdiction to adjudicate any dispute hereunder.

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If you agree with the terms and conditions of this Offer, please confirm your acceptance by executing this Offer below and returning to us one copy duly signed no later than the date mentioned in paragraph 13 above.

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SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: June 2, 2010

FORWARD-LOOKING STATEMENTS

This document may contain forward-looking statements. These statements are statements that are not historical facts, and are based on management’s current view and estimates of future economic circumstances, industry conditions, company performance and financial results. The words “anticipates”, “believes”, “estimates”, “expects”, “plans” and similar expressions, as they relate to the company, are intended to identify forward-looking statements. Statements regarding the declaration or payment of dividends, the implementation of principal operating and financing strategies and capital expenditure plans, the direction of future operations and the factors or trends affecting financial condition, liquidity or results of operations are examples of forward-looking statements. Such statements reflect the current views of management and are subject to a number of risks and uncertainties. There is no guarantee that the expected events, trends or results will actually occur. The statements are based on many assumptions and factors, including general economic and market conditions, industry conditions, and operating factors. Any changes in such assumptions or factors could cause actual results to differ materially from current expectations.