The report claims that the Lions have made an enquiry for the Nigerian international and that they will make an offer depending on the response.
The Istanbul giants have made strengthening central midfield a priority following the sale of Felipe Melo to Inter on transfer deadline day over the summer.
The Lions did sign Kevin Grosskreutz as his replacement but failed to register him before the end of the summer window and the World Cup winner is reported to be keen on leaving after growing increasingly disenfranchised with the club after sitting out the last six-months on the sidelines.
The Istanbul giants have been closely linked with Mikel in the past and the 28-year-old could be temped into making the move in pursuit of more regular first team football.
Mikel has made just nine appearances in all competitions for Chelsea this season but does have another two-years left on his contract.