Tevez, 27, was due to return to Eastlands on Thursday following a summer in which he has made clear his desire to leave the club for family reasons.
He is now expected back on Monday, having missed the club's pre-season tour of the United States - and an open training session at the Etihad Stadium on Wednesday.
In June he was quoted as saying he would never return to Manchester "even on vacation" but, after watching a £40 million move to Corinthians fall through, he is now faced with the prospect of continuing his career with City.
"Carlos has now been given extended leave so he can return on Monday, which is 21 days after Argentina's exit from the Copa America," said a Manchester City spokesman.
Inter Milan have been heavily linked with a move for Tevez ever since he was pictured shaking hands with Marco Branca, the head of technical staff at the club. There has been no offer forthcoming, however, with reports suggesting that any bid hinges on the future of Manchester United target Wesley Sneijder, whose sale would free up funds.
City have signed forward Sergio Aguero this summer for £38 million, a move that suggested they expected to be without Tevez in August.
Tevez is yet to be officially stripped of the City captaincy by boss Roberto Mancini, but it is expected defender Vincent Kompany will lead them out next season, as he has during pre-season.