Bulut is under pressure at Fener as they battle through a poor run of results.
And BILD says via Fotboll Transfers that Fener are considering removing Bulut and replacing him with a more experienced name.
Wenger has been discussed, along with Fener icon Christoph Daum. Istanbul BB coach Okan Buruk is also being linked with the job.
Should Wenger agree to the move, it would mean a reunion with former Gunners midfielder Mesut Ozil. It was Wenger who pushed to sign Ozil from Real Madrid for Arsenal, with the pair spending over five years together before the Frenchman stepped down. Wenger hasn't coached since leaving the Londoners in 2018.
Ozil left the Gunners for Fener at the end of January and is now reaching full match fitness in Turkey, having not played for Arsenal since March last year.
- updated March 1