The France international has fallen out of favour at the Etihad Stadium, with City boss Roberto Mancini branding Nasri "half the player he was last season".
The former-Marseille playmaker joined City in a £25m deal from Arsenal in the summer of 2011, but could be offered an escape route to Italy by Inter at the end of the season.
The Serie 'A' club are scouring the market for a replacement for Wesley Sneijder, after the Dutchman joined Galatasaray in the January transfer window.
And the Metro reports that Inter would be willing to pay up to £20m to sign the Frenchman in the summer.
The 25-year-old is reportedly considering his options and could be set to leave City at the end of the season, after a difficult six months in Manchester.
Roberto Mancini publicly questioned his attitude in an interview with the Guardian newspaper last week, suggesting Nasri has not lived up to his undoubted potential.
He's scored just one Premier League goal this campaign, but he's been in and out of the City first-team.
Still, his reptuation remains strong on the continent, and reports in Italy suggest Inter could face competition from big-spending French club Paris St-Germain for his signature.
Nasri is under contract with City until 2015, and the report claims City could sanction a season-long loan move for Nasri next term, if no club is willing to meet their valuation for the player.