Milan vice-president Adriano Galliani announced on Friday night that the club were dropping their interest in signing the Argentinian in the current transfer window after completing a deal for Maxi Lopez from Catania.
With Paris Saint-Germain and Inter Milan - the other two clubs heavily linked with Tevez this month - having also pulled out of negotiations, the 27-year-old striker may now have to stay at City.
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."
Joorabchian also claimed a rift with manager Roberto Mancini has been at the heart of Tevez's dispute with City.
The former Manchester United and West Ham forward first agitated for a move in December 2010 but at the time stressed he had no personal issues with Mancini, who took charge 12 months previously.
That position, however, appears to have worsened significantly since.
Joorabchian said: "The relationship with Mancini, ever since Mancini came into the football club, has not been good.
"You think about last Christmas when Carlos wanted to leave and it was all to do with feuds with the manager, and I think that just carried on and on.
"There was a point when Carlos did say, 'I can't get on here'."
Carlo Ancelotti remains hopeful that Paris Saint-Germain could yet sign Tevez in the future.
Ambitious French side PSG held talks with Tevez and his representatives earlier this week before ending their interest in the Argentine after failing to agree terms.
Tevez's representative Joorabchian has confirmed there is a possibility of the deal being reignited in the summer and Ancelotti would relish the chance to sign the 27-year-old.
The recently-appointed PSG boss is confident Tevez would be happy to play for the club after admitting it is not currently the right time to finalise a deal.
"About Tevez, it is over," Ancelotti said. "For later, I can't say. Maybe there will be another opportunity.
"In the future we will have to sign a forward.
"We talked with him and he said he would be happy to play for PSG.
"But, when no agreement is found...Finally, the club decided it was not a good opportunity."
