Fenerbahce sporting director Damien Comolli met with Arsene Wenger last week and discussed the possibility of the French manager taking charge of the club.
A source close to Comolli revealed to Turkish-Football that he held a meeting with Wenger.
Fenerbahce recently sacked Phillip Cocu and currently have assistant manager Erwin Koeman as head coach.
Koeman is not seen as a long-term option and this is not the first time the Yellow Canaries have flirted with the idea of Wenger taking charge.
Comolli knows Wenger after spending seven seasons at Arsenal from 1996.
Fenerbahce did consult the French manager after Ali Koc won the club presidential election but did not make a formal offer.
Koc has worked closely with former Arsenal vice-chairman David Dein for years and they have discussed the possibility of Wenger being appointed manager.
The 69-year-old manager is currently enjoying a break from management after spending 1996-2018 in charge of Arsenal.
Fenerbahce got their season off to an awful start under the stewardship of Cocu and are currently 13th in the league on 13 points.
The Istanbul giants are however, confident that they will be able to turn their fortunes around as they are in a transition phase.