The Mirror reports that the Turkish side plot a £6million swoop for the former Arsenal captain.
Bursaspor hope to conclude a deal for Toure in the next few days.
Toure is keen on leaving City this summer.
Bursaspor boss Ertugrul Saglam said: “We have been in talks with Kolo Toure over the past two days.
“It would be one of the most important transfers to be completed by an Anatolian side. Obviously nothing is certain until he signs pen to paper.
“However, we are working hard to try to finalize a deal.”