The bombshell story was broken by the Sun on Tuesday morning, with agent Dimitry Seluk claiming City did not make Toure feel valued and appreciated, especially on his 31st birthday which clashed with a party in Abu Dhabi to celebrate City's title triumph.
Seluk said there was "a big possibility" Toure could leave the club because of how the club acted.
The veracity of the story was thrown into doubt by the subsequent emergence of footage showing that the club produced a birthday cake for Toure during a team flight to the Middle East and the club also tweeted their birthday wishes to the midfielder.
However, Seluk has subsequently told the BBC that such treatment was not nearly respectful enough to Toure.
"None of them shook his hand on his birthday. It's really sick you know," he said.
"He got a cake but when it was Roberto Carlos's birthday, the president of Anzhi gave him a Bugatti.
"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."
In the video footage of Toure being presented with the cake, Toure sits motionless with his headphones on as Samir Nasri seemingly tries to cheer him up by clapping along while the cabin crew sing 'Happy Birthday."
However, according to Seluk, none of the team's players showed any respect to Toure.
"It is an important human relationship to shake hands and say 'happy birthday' but nobody did it to Yaya. It shows they don't care about him.
"I hear one newspaper has written that City congratulated him from Twitter but this is a joke. It is better they don't put anything on Twitter if they are not saying anything to him.
"The club's owners ate a 100kg cake after winning the Premier League this season but when they and the players were all together, none of them shook his hand on his birthday.
"If they don't respect him, then easy - Yaya will leave. No problem."