Unsettled Tevez wants to leave City after two years with the club and has cited family reasons, saying last week that he wants to be closer to his two children and their mother, who live in Argentina.
It initially seemed a fanciful prospect that Tevez would be able to move to South America, as no club was believed to have the financial clout to sign him from City.
However, the offer from Sao Paulo club Corinthians may interest City.
It would mean 27-year-old Tevez joining a team who are not their rivals in any competition, and he would be rejoining the club he played for from 2004 to 2006, before making a controversial move to West Ham.
Until Corinthians made their interest known to City, Tevez looked certain to remain in Europe, possibly in Spain or Italy, with a club such as Real Madrid or AC Milan, both potential Champions League rivals of City in the coming season.
Finding a club with the funds to buy the Argentina international, and space in their squad for him, promised to be a difficult task but the offer from Corinthians may give Tevez an escape route.
Tevez has scored 53 goals in 86 appearances for City since joining from neighbours Manchester United. Despite struggling for form towards the end of last season still finished level with Dimitar Berbatov as leading scorer in the Barclays Premier League as City finished third.