City thought a £40m deal had been agreed for the Argentine striker after he told the Premier League outfit he wanted to return to South America.
But Corinthians said there was not enough time to sign the the 27-year-old before the Brazilian transfer window closes at 0400 BST on Thursday.
Corinthians still want Tevez and hinted an agreement can be reached in January.
It had appeared that the former West Ham forward had got his wish for a transfer but then in a statement, Corinthians said: "The board of Sporting Club Corinthians hereby officially announce the impossibility of hiring the Argentine striker Carlos Tevez.
"While acknowledging the efforts of Manchester City and all involved in the negotiation, more time is needed for the transfer to be achieved, given that the window to sign players from abroad closes on Wednesday, 20 July [Brazilian time].
"We are aware of the dream our fans had of having this player at Corinthians again and we look forward to him being with us in the near future."
That would indicate that Corinthians may look to revive the deal in the January transfer window, although that would not be the preferred option of Tevez or his current club.
Tevez, who had a spell at Corinthians from 2005 to 2006, originally asked City for a transfer in December and has since reiterated that desire to leave so he can be closer to his family in Argentina.
However, there are few clubs who can match the asking price of about £40m.
Corinthians' move for Tevez - which emerged on Monday - was believed to be funded by a new television deal for Brazilian clubs.
But the Sao Paulo side's response to City's demand for a proper payment schedule on Tuesday was perhaps a sign the transfer would not have gone smoothly.
The breakdown of Tevez's transfer to Corinthians also leaves City manager Roberto Mancini's proposed move for Atletico Madrid striker Sergio Aguero in doubt.
Tevez, who is contracted to City until 2014, has been a key player for the club since arriving from neighbours Manchester United in 2009.
He helped Mancini's side to FA Cup success and Champions League qualification in the 2010/2011 campaign. He has scored 43 Premier League goals in his two seasons at City - the highest total of any player in the top division.
Carlos Tevez's move from Manchester City to Corinthians has fallen through because the Brazilian club pulled out.