Toure is out of contract at City this summer and it is unlikely he will be offered a new deal to extend his stay at the Etihad Stadium.
The news has alerted a host of clubs across Europe to Toure's availability on a free transfer this summer.
Liverpool are thought to be ready to offer Toure the chance to stay in the Premier League with Brendan Rodgers in the market for defensive reinforcements.
Rodgers is losing Jamie Carragher to retirement, while there has been speculation over the futures of Martin Skrtel and Sebastian Coates.
Toure would help fill the void left by Carragher and provide the necessary experience to what is a youthful side at Anfield.
The 32-year-old has made 17 appearances in all competitions for City this season with the centre-back seeing his first-team chances limited by the form of Matija Nastasic alongside captain Vincent Kompany.
Toure has a wealth of Premier League experience having made over 400 appearances during his time in England and has won the Premier League title with both City and Arsenal.