Criteria, which is Caixabank's largest shareholder with a stake of more than 30%, already owns around 5% of Telefónica.
A 10% stake in Telefónica is worth about 2.38 billion euros ($2.58 billion) at the current market price.
The Spanish government on Monday completed the purchase of its 10% stake to counter the acquisition of a similar stake in Telefonica by Saudi Arabia's STC.
Criteria declined to comment on the information.
(1 U.S. dollar = 0.9210 euros)
(Reporting by Inti Landauro and Jesús Aguado; edited by David Goodman; edited in Spanish by Mireia Merino)