Following two hours of discussions in Milan with Tevez's agent Kia Joorabchian, the Italian champions sent their offer to City, asking for a loan until the end of the season with an option to buy the 27-year-old in the summer.
To make the deal happen, AC Milan chief executive Adriano Galliani said Tevez has agreed to make a big economic sacrifice.
"He's renounced a mountain of money. We have an agreement with the player and we've sent an email to City with a proposal," said Galliani.
"He's not playing, he's a great player and if he does well with us we'll recompense him for that ... Tevez wants to join us, half the deal is done and now we'll wait for City's reply."
City manager Roberto Mancini has already spoken of his desire to get rid of the Argentinian following claims he refused to come on as a substitute in a Champions League match against Bayern Munich.
City found Tevez guilty of five breaches of his contract for refusing to warm up in that match, which took place in September.
"I don't know what the situation is with Carlos at this moment," Mancini said.
"I think that for us it is important to sell him. We can do this for him and for the club. If he has the chance to go to Italy, I am happy for him."
There is no guarantee, however, that City will accept Milan's proposal which is believed to be considerably less than the one they accepted from Brazilians Corinthians in August.
Italian press claim the eventual sum Milan are offering for a permanent transfer is 20 million euros ($A26.3m), less than half the amount City accepted from Corinthians.
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