The 32-year-old Ivory Coast international is approaching the end of his contract at the Etihad Stadium, and with no new deal on the table could walk away on a free transfer.
Toure has made just 16 appearances for Roberto Mancini's first-team this season, and is eager to play more regular football, which could prompt him to seek a new challenge away from the Premier League.
The Manchester City stopper has attracted interest from a number of different clubs around Europe, with Paris Saint-Germain, Galatasaray and Fenerbahce all said to be monitoring the African stopper's situation in England.
Last month, Toure talked up the possibility of a move to France with Monaco believed to be his preferred destination over current Ligue 1 leaders PSG.
"Monaco are a great club that want to progress like Paris," he told L'Equipe. "It can be a very good option indeed with my experience."
However, AC Milan are believed to be lining up a rival bid for the Manchester City star, which could see him reunited with former team-mate Mario Balotelli at the San Siro.
The Serie 'A' giants are set to introduce a new transfer policy which places an emphasis on buying young, up and coming talent, but will also look to add experience with bargain buys and Bosman free transfers.