French international Mangala spent last season on loan with Valencia in La Liga, making 33 appearances in all competitions for the Spanish side.
The defender has not featured at all for the 'Citizens' under Pep Guardiola, though he has been on the bench for City's first two games of the new Premier League season.
The 26-year-old joined City in 2014 from Porto for a fee of £32m but it appears that much like Joe Hart, Guardiola has decided that he is not good enough on the ball for his possession-based system.
City are hoping to replace the Frenchman with West Brom's Jonny Evans, though Tony Pulis' side are demanding £35m for the former Manchester United man.
Inter, for their part, are keen to strengthen their back line as they look to re-establish themselves as Serie A giants and have also been linked with a surprise move for Arsenal's Shkodran Mustafi.