Toure is out of contract at the end of the season and has been approached by clubs from China who have been splashing on a host of star signings in recent months.
Manchester City's title hopes hit by Everton at Goodison Park
He snubbed those offers during the summer transfer window and gave the same response when he was contacted again this month because he would prefer to continue playing in England, the British media reported.
It remains unclear whether City, who signed Toure from Barcelona in 2010, will offer him a new deal.
Toure has regained his place in the heart of City's midfield over the past two months after a row between the club and his agent threatened to end his time at the club.
Guardiola admits lack of ‘rhythm’ after home draw against Saints
Toure was frozen out by manager Pep Guardiola after his outspoken representative Dimitri Seluk claimed the midfielder had been humiliated by his omission from City's Champions League squad.
That situation was resolved with an apology from Toure in November.
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