The Istanbul giants sit on top of the Turkish Super League and are chasing a place in the last 16 of the Champions League, but are in need of an experienced centre back.
Toure was closely linked with a number of Turkish clubs this summer with Bursaspor reported to have agreed to a 3.5 million euros deal at one stage.
However, the move fell through when the Green Crocodiles were unable to meet the Ivory Coast international's wage demands.
The 31-year-old defender has six months left on his contract at the Etihad Stadium and City are unlikely to renew terms unless he accepts a wage cut and a reduced role in the team.
Toure has only featured in four Premier League games and could be allowed to leave if Roberto Mancini were to sign a centre back in the January transfer window.