The powerful defender has been heavily linked with the Turkish giants in recent days, amid rumours that he no longer has a future under Manuel Pellegrini.
Lescott was a key member of the Sky Blues’ title-winning side in 2012, but has since struggled to hold down a starting berth.
With his contract due to expire in six months’ time, it has been speculated that he will be allowed to leave the club in the coming weeks for a minimal fee.
However, Pellegrini is ready to battle to keep the 31-year-old as he plots to maintain his side’s push for the quadruple.
City are firmly in hunt for the title, are still present in both the Champions League and Capital One Cup and will kick off their FA Cup campaign over the weekend.
With Pellegrini confident of success in every competition, he knows that he will need a vast squad at his disposal, and feels that Lescott can still contribute.
It’s unlikely that the club will make serious efforts to extent the experienced enforcer’s £90,000-per-week deal, which will leave him free to discuss a Bosman deal with other teams for the summer.