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FORM 6-K

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

Report of Foreign Private Issuer

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

of the Securities Exchange Act of 1934

For the month of August, 2014

Commission File Number: 001-09531

Telefónica, S.A.

(Translation of registrant’s name into English)

Distrito Telefónica, Ronda de la Comunicación s/n,

28050 Madrid, Spain

3491-482 87 00

(Address of principal executive offices)

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

Form 20-F  x            Form 40-F  ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1):

Yes  ¨            No   x

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7):

Yes  ¨            No   x

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

Yes  ¨            No   x

If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): N/A

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Telefónica, S.A.

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RAMIRO SÁNCHEZ DE LERÍN GARCÍA-OVIES

Secretary General and

of the Board of Directors

TELEFÓNICA, S.A.

TELEFÓNICA, S.A. as provided in article 82 of the Spanish Securities Market Act (Ley del Mercado de Valores), hereby reports the following

SIGNIFICANT EVENT

Telefónica, S.A. and Telefónica Brasil, S.A. have submitted to Vivendi, S.A. an offer (the “Offer”) for the combination of Telefónica Brasil, S.A. and Global Village Telecom, S.A. (GVT), by virtue of which Vivendi, S.A. would receive a consideration in cash of 11,962 million Brazilian Reais and newly issued shares representing 12% of the share capital of Telefónica Brasil, S.A. after its combination with GVT. Thus, the amount of the Offer, according to the current market price of Telefónica Brasil, S.A., amounts to a total of 20,100 million Brazilian Reais (equivalent to 6,700 million euros at current exchange rates). The cash consideration would be funded through a capital increase at Telefónica Brasil, S.A. in which Telefónica, S.A. would subscribe its proportional share, funded, in turn, through a capital increase.

The Offer envisages that, should Vivendi, S.A. be interested in acquiring a stable stake in Telecom Italia, S.p.A. (“Telecom Italia”), Telefónica, S.A. would offer to Vivendi, S.A. the acquisition, in cash, up to 1,110 million ordinary shares of Telecom Italia, currently representing a stake of 8.3% of Telecom Italia voting share capital, directly or through a mandatory convertible instrument. The transfer of the shares would take place at closing of the transaction between Vivendi, S.A. and Telefónica Brasil, S.A.

According to the terms of the Offer, it expires on September 3, 2014, unless it is previously accepted by Vivendi, S.A., or if the bidders decide to extend the Offer’s validity period.

The Offer is subject to obtaining the relevant regulatory authorizations (including telecommunications and anti-trust) and to the fulfilment of other customary conditions in this type of transactions.

Telefónica Brasil, S.A. is the leader in the mobile wireless market and the leading broadband operator in the city of Sao Paulo. GVT is the most successful and fastest growing alternative operator in Brazil. A combination of both companies would create the largest telecom operator in the largest market in Latin America, providing a unique platform for the generation of synergies and value creation.

Madrid, August 5, 2014

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SIGNATURES

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.