Milan vice-president Adriano Galliani announced on Friday night the club were dropping their interest in signing the Argentinian in the current transfer window after completing a deal for Maxi Lopez from Catania.
Galliani told Milan Channel the Italian champions had set a deadline of 1900 local time for a final decision and said: "At 1830 I was convinced we were very close to sealing the Tevez deal. I did my best, it was a day where I had my heart in my mouth, but no more could be done. We had everything set for Tevez to come, but the situation changed."
But he added: "Today was still very important because we have solved some misunderstandings of recent days with City, relations are much improved.
"But, patience - life goes on. The market will reopen in four months - we'll see."
Tevez has been in Argentina without City's permission since November hoping to secure a move away and has not played since September.
City chairman Khaldoon al-Mubarak said this week the player would not be sold below the club's valuation, which is believed to be around ?25million.
Tevez's advisor Kia Joorabchian admitted earlier on Friday the prospect of a return to City was growing because no club had made an offer acceptable to City.
Joorabchian told talkSPORT: "We've been in negotiations with three big clubs. I don't think anyone has reached the numbers City were hoping for.
"At the moment it looks like Carlos will remain at City until this summer."