The Turkish side's supremo expects a deal to be struck before the end of the January transfer window, with the forward tipped to pen a lucrative contract at the Inonu
The 31-year-old is out of contract at the end of the season and recently announced he will not renew his stay with the Ligue 1 leaders, meaning he is free to talk to other teams with a view to signing a pre-contractual agreement.
Speculation in the Turkish media suggested that the Brazilian had already negotiated personal terms, and on Wednesday, the Black Eagles' supremo told NTVspor: "If our conditions are met, the transfer will happen."
Nene, who despite finishing as the French top flight's joint-top scorer with 21 goals last term, has been frozen out of Carlo Ancelotti's plans at PSG in 2012-13, featuring just nine times in the league.
The forward has reportedly been offered an annual net salary of €2.25 million [£1.8m] by Besiktas, who are seeking a replacement for the newly-departed Ricardo Quaresma.