According to Dimitri Seluk, who represents the Ivory Coast international, Toure was dismayed that, despite the club giving him a 31st birthday cake, the owners did not personally congratulate him at a post-season party in Abu Dhabi.
Former Barcelona powerhouse Toure, whose goals were instrumental in City's second title in three seasons, could even seek a move, Seluk said.
"He got a cake but when it was Roberto Carlos's birthday, the president of (Russian side) Anzhi (Makhachkala) gave him a Bugatti," Seluk told BBC Sport.
"I don't expect City to present Yaya with a Bugatti, we only asked that they shook his hand and said 'we congratulate you'. It is the minimum they must do when it is his birthday and the squad is all together.
"Of course Yaya is upset about this. It is his birthday and nobody said anything or shook his hand, so he does not feel comfortable," added Seluk, who said City sent a Twitter message wishing Toure a happy birthday.
"The most important thing is a human relationship and maybe this is his opportunity for Yaya to find that. If City don't respect him, then easy - Yaya will leave. No problem."
Toure, who joined City in 2010 as part of the owner Sheikh Mansour's vast outlay on world-class players, moved to reassure Man City fans via his Twitter page on Tuesday.
"Thanks for all the birthday messages today. Card from City just arrived... Must have got lost in the post. Haha" he Tweeted.
"Jokes aside. Please do not take words that do not come out of MY mouth seriously. Judge my commitment to @MCFC by my performances."
However, Toure later tweeted: "Everything Dimitry said is true. He speaks for me. I will give an interview after (the) World Cup to explain."
BARCA FINISH
He was also quoted in an interview with North American network beIN SPORTS in which he repeated his desire to finish his career at Barcelona, who sold him to City in 2010.
“I have said that in front of the camera before and I have said that to newspapers about ending my career there (Barcelona), but we don’t know because football is moving fast and you never know about tomorrow," Toure told beIN SPORTS.
“Because of the brilliant season Man City have had, everybody is talking about me and everything is open and we don’t know tomorrow, but my focus is on the World Cup and at the end of the World Cup we will see what happens.
“I think my agent, Dimitri, is always on the phone and he knows what he has to do because I trust him a lot. He knows what he has to do because we were always open about everything.”
Toure signed a new four-year contract last year and Seluk denied that he was looking for a better deal with the club.
"No. Money is not important. He has enough money," he said.
"It is more important he plays for a club that respects him more than having a few thousand pounds added to his salary.
"I have spoken to him about leaving and we will see what happens but, at the moment, Yaya is really upset."
(Reporting by Martyn Herman, editing by Julien Pretot)
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