The daily newspaper states that the Istanbul Giants are on the look-out for a midfielder to replace Felipe Melo who left 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.
Galatasaray have a long-standing interest in the Nigeria international and are hoping to strike a deal for him this winter.
Galatasaray are currently in fourth place with 26 points in 15 games and are managed by Mustafa Denizli. The Istanbul based club take on Akhisar Belediyespor this weekend.