Toure has fallen down the pecking order at the Etihad Stadium since a six-month ban for failing a drugs test and has been linked with a move away from the Premier League champions.
Now, his manager has declared that the defender has a decision to make over where his future lies, but has doubts over the Turkish club's ability to afford his salary.
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"It is up to Kolo to decide if he wants to go to Bursaspor or not," Mancini told The Sun. "However, can they meet his demands?"
The Ivorian made just eight Premier League starts in the 2011-12 campaign and despite his agent's claims that the 31-year-old's focus is on his current club, both Bursaspor and Saudi Arabian club Al-Hilal are rumoured to be monitoring his situation.