Toure has more than two years left on his current contract at the Etihad but City are desperate to keep their star midfielder and will up his wages to £220,000 a week to make it happen, according to the Daily Star.
City manager Roberto Mancini has expressed his desire to keep Toure and the enforcer has also gone on record as being keen to continue his Premier League career.
Toure told the Daily Star: "The Premier League is fantastic. I'm happy to be in this championship and I want to stay here a long time. I always want to be here."
The 29-year-old scored his 10th goal of the season in yesterday's 2-0 win over Chelsea.