Pepe, 34, is available on a free transfer this summer after leaving Real Madrid following the expiration of his contract.
The centre-back made 334 appearances during a 10-season spell at Real, winning three La Liga titles, two Copa del Rey crowns and three Champions Leagues in the Spanish capital.
In recent days, it has been claimed that Besiktas were on the verge of announcing a deal for Pepe, but the Turkish outfit's director of football operations has insisted that the club "are not in the final stage of this transfer".
"We are in the market to sign a world-class centre back and Pepe is one of the players any club would welcome with pleasure," Naibi told Goal.com. "But we are not in final stage for this transfer."
Paris Saint-Germain have also been strongly linked with a move for Pepe.