The report states that the Istanbul giants will make a move for the Nigeria international during the January transfer window.
Galatasaray have been on the look out for a midfielder to replace Felipe Melo who departed for Inter Milan in the summer.
Mikel has spent the majority of his football career with the Blues but has fallen down the pecking order behind the likes of Nemanja Matic and Ramires.
The 28-year-old whose contract expires in 2017, has made just five Premier League appearances for Chelsea this season.
The Istanbul Based club are currently in fourth place with 26 points in 15 games and are managed by Mustafa Denizli. Galatasaray take on Akhisar Belediyespor this weekend in the league.