The Ivorian has been linked with a move away from the Etihad at the end of the season as new manager Pep Guardiola looks to mould his squad.
The midfielder already has lucrative offers from China and the Middle East, while MLS teams are also interested.
However, according to Corriere dello Sport, Inter are hoping to persuade Toure to join them in the summer.
The Italian club are ready to offer the 32-year-old a two-year contract, with the option of a further year if both parties wish to extend his stay.
Inter boss Roberto Mancini worked with Toure during his time at Manchester City and is keen to link up with him again.