Ziyech had been set to complete a loan move to Paris Saint-Germain on deadline day, but the switch collapsed.
He is now facing the prospect of limited game time at Chelsea over the second half of the season unless he can secure a move to another league where the transfer window remains open.
Fenerbahce are free to sign Ziyech and they are now making a concerted effort to do so.
According to Turkish daily En Son Haber, Fenerbahce’s president Ali Koc has been in touch with Ziyech’s agent.
Koc has told Ziyech’s agent that his client is better making a loan move to Fenerbahce where he would be guaranteed a spot in the team than sitting on the bench at Chelsea.
Fenerbahce are battling for the Turkish Super Lig title and sit in second, six points off leaders Galatasaray, but with a game in hand.
Their game in hand comes this evening when they take on Adana Demirspor, where Roma legend Vincenzo Montella is in charge.
