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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 July, 2016

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

General Secretary and

Secretary to the Board of Directors

TELEFÓNICA, S.A.

TELEFÓNICA, S.A. as provided in article 228 of the Spanish Securities Market Act (Ley del Mercado de Valores), hereby reports the following

SIGNIFICANT EVENT

Telefónica, S.A. through its 100% subsidiary, Telefónica Internacional, S.A.U. (hereinafter “Telefonica”), has proceeded with the sale of 361,794,559 shares of China Unicom (Hong Kong) Limited (“China Unicom”), representing 1.51% of the share capital of the company, by a block trade process, at a price of HK$ 7.80 per share, for a total amount of HK$ 2,822 million, approximately € 322 million. Thus, Telefónica maintains a stake close to 1% in China Unicom.

This deal is part of Telefónica’s proactive management of its asset portfolio and its mid-term deleveraging objective. Telefonica maintains its commitment to the Strategic Alliance with China Unicom, recently strengthened through cooperation in digital areas such as the big data joint venture between both companies.

Madrid, July 10, 2016.

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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.