The 33-year-old Argentine former international has been a flop since moving this year to Shanghai Shenhua on a fat salary.
The 33-year-old Argentine former international has been a flop since moving this year to Shanghai Shenhua on a fat salary, scoring only twice, missing half the games through injury and having his commitment repeatedly questioned by fans.
Tevez, who has previously suggested he would look to leave after the season, flew to Buenos Aires this week for treatment on a muscle injury.
The trip has fuelled suspicions that he may not return, though the Chinese Super League (CSL) club told AFP this week Tevez was expected back by the end of the month.
Shanghai Shenhua made Tevez one of the best-paid players in the world when they signed him in January from Boca Juniors on reported weekly wages of around 730,000 euros ($850,000).
But the former Manchester United, Manchester City and Juventus star has failed to settle and has been christened by supporters and media in China as "Very Homesick Boy" -- a play on how his name is pronounced in Chinese.
The label is also an apparent reference to Tevez's falling-out with then-City boss Roberto Mancini, when Tevez refused to warm up as a substitute in the last moments of a Champions League match against Bayern Munich in September 2011.
Tevez flew back to Argentina and considered retiring, before eventually returning to England in February 2012.
Many football fans on Weibo, China's equivalent of Twitter, criticised Tevez.
"He won't need to come back in person. I'll deliver his luggage to logistics companies," said one posting.
"Tevez shamelessly went back to Argentina. Don't ever come back," said another.
"Shenhua's highest-paid yet worst foreign player. As a Shenhua fan since 1994, the club's management this season is the worst ever," added another.
Shenhua say that a break in the CSL season made it a good opportunity for Tevez to seek rehabilitation back in Argentina and that the decision to let him go was made after discussions between the player and the club's medical team.