Speaking during a press conference on City's pre-season tour of America, Mancini insisted that the wantaway Argentinian striker was free to discuss personal terms with Corinthians.
However, the Timao have now claimed that City have altered their valuation of Tevez and how any fee would be paid, leaving the Brazilians to re-evaluate the situation.
"Following news reports claiming an agreement had been reached between Corinthians and striker Carlos Tevez, the president Andres Sanchez is keen to come forward to clarify that Manchester City have not accepted the proposal by Corinthians," a statement on the club's official website read.
"In fact, the club sent a counter-proposal to Corinthians this morning that, due to the time difference, did not reach the attention of the board until now.
"In the counter-proposal, the Premier League club sought to change the structure of payment and the total value of the transaction. In addition, Manchester City also insist that Tevez gives up a pending amount with the English club.
"Finally, the president Andres Sanchez advises that there is nothing concrete at the current moment with Tevez and that City's counter-proposal will be reviewed by him and the board."
Corinthians reportedly had a £35 million bid rejected for Tevez last week.