Playmaker Toure looked to be on his way out of the Etihad Stadium this summer and was linked in reports with clubs including Inter Milan and Chelsea.
However agent Dimitri Seluk has confirmed Toure will remain at the club he joined from Barcelona five years ago.
Seluk said in the Sunday Mirror: " Yaya is staying - because Sheikh Mansour told him he must stay.
'Hopefully the president we choose will be OK' - Guardiola on Barca elections
"Mansour told Yaya that he is still a very important player and that he was the first big player to join City after the takeover.
"He told him that City wouldn't even discuss a sale.
"This is good. People have tried to say that Yaya only wanted more money, but it was never about money. It was only about respect."
Seluk had previously claimed Toure was "90 per cent certain" to leave City at the end of the season.
City boss Manuel Pellegrini repeatedly stated his desire to hang on to the Ivory Coast midfielder, with the 32-year-old having two seasons left on his contract.
The award for worst penalty of the season goes to... Wout Weghorst
Pique likely to miss Barca's clash with PSG due to knee injury