The Serbian left-back joined City from Lazio in 2010, but has fallen behind Gael Clichy in the pecking order at the Etihad Stadium.
And Inter Milan, who finished down in 9th in Serie 'A' last term, hope to lure Kolarov back to Italy with the promise of first team football.
Kolarov has made just 20 Premier League starts in the past 24 months, but the 27-year-old would have to take a pay cut to join Inter.
Reports in Italy claim the Italian giants believe they stand a chance of landing the full-back, but Kolarov stands to earn £10m over the next two years of his City contract.
But with a new manager, thought to be Manuel Pellegrini, expected to be named as City's new boss in the next few weeks, Kolarov may find himself frozen out of the first team again next term.
And the report claims he may opt to return to Serie 'A' in a bid to secure regular match action.
The free-kick specialist spent three seasons in Italy with Lazio.