Toure turned 31 on May 13, just days after City sealed their second Premier League title in three seasons.
His agent Dimitri Seluk, who has previously accused City of a lack of respect for the attacking midfielder, claimed an exit was on the cards as a result of the supposed birthday snub.
"There is a big possibility Yaya will leave this summer. He is very upset. What happened at his birthday means the club don't care about him. It was proof," Seluk told The Sun.
"They can say whatever they want, 'Oh we like him but we forgot'. Forgot? About Yaya? The player who helped you to be two-times Premier League champions? The guy who helped you win the FA Cup and League Cup?
"In a normal team, his team-mates and club would at least give him good wishes. But when you win the title and two days later you have a big party to celebrate the title and nobody comes to Yaya to say happy birthday, what more do you want?"
It remains to be seen whether Seluk is true to his word, or potentially chasing a new and improved contract, with Toure having completed one year of his current four-year deal.
Seluk was quoted in March 2013 as claiming 'only Roberto Mancini respects Yaya', although the Ivory Coast international has stayed on at the club under new manager Manuel Pellegrini, and has performed superbly over an extended period of time.
Still, the agent continued by saying: "If a player like Yaya went to Liverpool and they won the league for the first time in 24 years, Yaya would be a god in Liverpool.
"But at City, Yaya is no hero. He's nobody. That's how the club make him feel. He's very upset and he started thinking about leaving the club. And he will leave if things carry on like this.
"We're not doing this for more money. We probably can go for less money to another club. If they think they can buy everything, they are wrong. I think these people don't care. Only stupid people would want Yaya to leave."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.