Off contract in June, the Belgium international has been linked to a pre-contract agreement with Besiktas in recent days.
But Besiktas comms chief Candas Tolga Isik has played down the rumours - and even insists they do not need Fellaini.
He told Goal: "I am responsible for communication, not transfers, but I'm not involved in transfers until they let me know.
"My job starts when they decide to sign a player. I do not know anything about Fellaini, I'm not sure we need a player in that position: we have Medel, Atiba, Öguzhan, Tolgay and Necip."