The Sun says the Italian giants know Richards faces a fight for game time at the Etihad next season.
City have indicated they are willing to hand the 25-year-old a new deal, even though he still has two years left on his current one.
But he can expect a huge battle for first-team football next season, with Pablo Zabaleta and Maicon also vying for the right-back spot.
Inter would be willing to sign the England star outright.
But if he was to pen a new deal the Italians may still try to take him on loan.