Toure's agent wants City to offer the 32 year-old, a new three-year deal or allow him to leave on a free transfer.
Another option could be to take the path of breaking his City deal, in the way Scottish defender Andy Webster quit Hearts to join Wigan in 2006.
Toure will be entering the fourth year of the improved four-year contract he signed in 2013, putting him outside what world governing body FIFA defines as a 'protected period'.
He would be entitled to move under article 17 - titled 'consequences of terminating a contract without just cause' - of FIFA's transfer regulations, but would have to pay substantial compensation.
Agent Dimitri Seluk said in the Sunday Mirror that City had put off contract talks until the summer.
"This is unacceptable. A player like Yaya Toure should not be moving towards the last year of his contract wondering if he is going to get a new deal," Seluk said.
"He is 32. He has three or four years left at the top and City must tell Yaya now what they want to do. The best idea would be to give Yaya a three-year contact that will keep him at the club for the rest of his career. The second is to say 'thank you' and allow him to leave for nothing."
Seluk said Toure wants another Champions League title, having won that competition with Barcelona in 2009, a year before he joined City on an initial five-year deal.
"But I will not let Yaya waste a year at City," Seluk said. "I will not let City keep him because, in one more year, his chances of joining another big club will be smaller.
"I will go to FIFA. I will write to them and tell them that we will buy Yaya out of his contract. We can do this. It is an option. This is not a threat. I promise you that Yaya will leave City this summer one way or another if they don't offer him a new contract."