Reports suggest Toure's representative Dimitri Seluk has given City an ultimatum, saying his client will leave the club this summer if he is not offered a new deal by the weekend.
"If he signs a contract in the next three or four days, OK. If not, we will not wait any longer and will start negotiations with different clubs," Seluk was quoted by The Sun on Tuesday.
"Today is Tuesday, so it means by Saturday. We will say 'Thank you. OK, Yaya will leave in May'.
"I do not feel he will stay at City. This is not about money. He wants to leave because of many reasons.