The Ivorian, 29, was furious with City and threatened to buy out his contract and leave the club in the summer if he is not offered a new deal by Saturday. Toure still has two years left on his contract he signed when he moved to the Etihad from Barcelona in July 2010.
City chiefs said they will fight to keep Toure for the long-term but are yet to come up with the offer.
However, this situation has alerted Europe's biggest clubs who feel Toure is the best in his position. Clubs like Chelsea and Real Madrid are ready to offer Toure his current £220,000-a-week wages while potential buyers will have to shell out £22million for the midfielder.
City are also planning a huge clear-out during the summer which would see players like Joleon Lescott, Carlos Tevez, Edin Dzeko, Aleksander Kolarov and Kolo Toure move away from tht Etihad.
Tevez, 29, is eyeing a return to Argentina with Boca Juniors while Dzeko could back to the Bundeliga with Werder Bremen, Wolsburg and Bayern Munich interested. Lescott, who has fallen down the pecking order at City, could make a return to former side Everton.
David Silva, who arrived at City at the same time as Toure, signed a new improved deal back in September. City also tabled an offer for Toure last summer but have now stalled and the deal is not yet finalised.