The Italian outfit have been repeatedly linked with a move for the 33-year-old, who has just one year remaining on his contract at the Etihad Stadium.
Incoming manager Pep Guardiola has already sold Toure once during their time together at Barcelona, and he is expected to do so again as he continues to revamp his squad.
Reports have also suggested that Toure could join Chinese outfit Jiangsu Suning before moving to Inter on loan, with both clubs sharing the same owners.