The Portuguese boss is set to replace Ismail Kartal at the Turkish giants, according to Gianluca Di Marzio, in what would be his 11th managerial role.
Mourinho succeeds the Turkish boss after Fener finished second in the Turkish Super Lig for the third successive year.
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The former Manchester United boss is to return to the game after being sacked by Roma in January after two-and-a-half years.
It had been previously reported that Mourinho was a target of Saudi Arabian club Al Qadsiah, but his next destination is Turkey.
The news comes just a day after it was revealed that the 61-year-old manager will join TNT Sports for the coverage of the Champions League final on Saturday 1 June.
‘The Special One’ had expressed interest in returning to management and looks to have secured a job after five months out of the game.