According to a report from Turkish outlet fotoMac, the Istanbul giants are keen on signing the Serbian on loan, with the deal also having a £6.8 million option to make the deal permanent.
Reports from Turkey add that Fenerbahce have offered Mitrovic a salary of around £2.6 million per year, with this increasing with add-ons that are set to be inserted into his contract.
Fulham are yet to respond to this offer, and with him enduring a difficult season in the Premier League, scoring just three goals and providing three assists in the league, he could be set to leave Craven Cottage.
The Turkish reports also add that the 26-year-old does not want to play in the Championship, and that he is set for a move this summer.
Ever since joining Fulham on loan from Newcastle United in January 2018, and then made his move permanent, Mitrovic has scored a staggering 53 goals in 131 games for Fulham, yet plenty of them came in the Championship.
This season, he was often left out of the side by Scott Parker, with the English manager rotating him with the likes of Josh Maja, Ivan Cavaleiro and Ademola Lookman.