The Ivorian's representative has set the Premier League champions a deadline for a new contract to be offered, but the club are determined not to open discussions until the summer
Toure's current deal runs until the summer of 2015, but under Fifa rules he is able to buy out the remainder of his contract and seek a new club from this summer onwards.
Dimitri Seluk, the 29-year-old's representative, claimed City have until the weekend to offer his client an extension, or he will look elsewhere at the end of the season.
“If he signs a contract in the next three or four days, OK," Seluk told the Sun. "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.”
But despite Seluk's ultimatum, Txiki Begiristain and the rest of the City board are determined not to be bullied. In October, Goal.com revealed the club had elected not to begin contract discussions with Toure and his representatives until the summer.
That resolve has not wavered, and is unlikely to be shaken by Seluk, who has a history of posturing - last summer he claimed Toure was leaving to re-join Barcelona.
The 29-year-old is already one of the top earners at City, with a basic wage of €175,000-a-week rising to €257,000 after bonuses.