The Ivorian is out of contract in the summer and he looks set to leave the Etihad after spending eight years there.
The 34-year-old is said to already have lucrative offers on the table from clubs in China, but he is open to staying in Europe.
And, according to Turkish newspaper Takvim, Fenerbahce are closely monitoring Toure’s situation.
The Turkish club are looking to make a statement signing this summer and the midfielder is considered a viable target.