Toure has reportedly been in talks with the Turkish giants about a move ahead of their country's transfer deadline on Wednesday night.
But the 31-year-old, who has just a year left on his City contract, could now see his value fall due to being ineligible for Europe's elite club competition.
Meanwhile, City captain Vincent Kompany is convinced the Premier League champions will be ready for the tough Champions League assignment awaiting them.
Roberto Mancini's men have been drawn alongside Real Madrid, Ajax and Borussia Dortmund, the champions of Spain, Holland and Germany respectively, in the group stages.
City failed to progress beyond the first round last season after coming up against Bayern Munich, Napoli and Villarreal and the task could be even harder this time.
But Kompany said: "That is why you are in the Champions League. I thought it couldn't get much more difficult than last season but here you go. It is a great challenge.
"I do think we are the kind of team that gets better as the challenges are greater. That is perfect for us. There won't be any moments where we will be surprised.
"The motivation will always be sky-high. The atmosphere will be great in each of the six games we have in the group. I couldn't think of a better way to play the Champions League."
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.