Toure's representative Dimitri Seluk says talks have been ongoing for six months over an extension to his current deal, which runs to 2015.
Dimitri Seluk: "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.
"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.
"He is one of the best players at Manchester City but does not feel the respect of the staff. Only Roberto Mancini respects Yaya."
"It's all strange. It's not normal to have negotiations for six months about a contract.
"They have been talking about small details all this time."
"Maybe if the owner speaks to Yaya, maybe he doesn't know the details."