How? By using the money to buy former Red Devil Paul Pogba.
Even the most ardent City fan will admit Toure's behaviour is pretty unfathomable, and is doing himself a disservice - and the club should not be held to ransom by a player already earning in the region of £200,000 per week, no matter his immense talent.
Toure's on pitch dominance gives them incentive to play tough and hold onto him, but they do perhaps have an opportunity.
Rivals fans at United will no doubt be hoping the midfielder who has dominated them so regularly is sold, but the smiles will be wiped from their faces if City move to sign Paul Pogba as a replacement.
Pogba is the former United academy star who left on a free when his contract expired, and has blossomed into Europe's most in-demand midfielder, with values of around £50 million touted for his services.
Seeing their former protege in a City shirt would be an unpleasant sight for United fans, and for the reigning Premier League champions it could be a long-term upgrade.
Financial Fair Play would restrict City from making a move for Pogba under usual circumstances, but if they were to sell Yaya Toure to the highest bidder, their net spend on the Frenchman would not be one to cause concern.
Pogba is a player who can be the same type of powerful midfield force Toure is, with similar long range shooting ability. He is also 10 years younger than the 31-year-old Ivorian.
City may not like their star player agitating to force a potential transfer, but if they can fetch a large price, and sign a superstar replacement, it has to be viewed as a viable opportunity.