The Rossoneri's offer also included a commitment to buy Tevez for £21million next summer, but City are adamant Tevez will only leave the Etihad Stadium on a permanent deal.
Paris Saint-Germain have agreed a £21m deal with City for the Argentina striker, and City owner Sheik Mansour is understood to have a close relationship with PSG's Qatari owners.
It is clear that Tevez would prefer a move to Milan and it could cause yet another disagreement with officials at City.
Milan chief executive Adriano Galliani told Italian media that a loan deal looked out of the question.
He said: 'Manchester City want us to buy Tevez definitively. 'We have suggested that we sign the player on loan, with an option to purchase.
We're not changing our position. 'It's going to be a long negotiation. Anything can happen in the transfer market.'
City had signed Tevez from rivals Manchester United in 2009 and the former West Ham forward is now on the verge of leaving Eastlands.
The Argentine striker was found guilty by the club of five breaches of his contract, and has since returned to Argentina without City's permission.