Tevez's representative Joorabchian has been in talks with the Brazilian club after they lodged an offer of around ?35million.
City have not yet responded to Corinthians, as they consider whether to sell their talismanic, yet unhappy, captain.
The transfer deadline for permanent deals in Brazil is July 20, so Corinthians are pushing for a quick response.
Tevez, dropped for Argentina's 3-0 Copa America win over Costa Rica on Monday, declared earlier this month that he wished to leave City for the sake of his family.
With none of Europe's leading clubs apparently interested in spending ?50million to sign the City captain, it was starting to look like Tevez might spend next season at the renamed Etihad Stadium after all.
However, news has now arrived of Corinthians' interest with Tevez telling Telefe: "If there is interest, I don't have any problem in returning to Corinthians."
Joorabcian feels that the transfer is 'close' to being completed.
"Negotiations have already begun. Corinthians are in contact with us," said Joorabchian.
"His [Tevez's] dream and mine is to see him back with Corinthians. He said he has a job that does not end there, he wants to return because he has the dream of winning the Copa Libertadores.
"Corinthians have made the offer, now it depends only on Manchester City. The City has to make a decision.
"Everybody is working to make this happen, I, Corinthians, Tevez, Adrian Ruocco (the other agent who work on Tevez).
"It is impossible to determine the situation, but I think it's close."
Joorabchian insists that Tevez would only consider playing for two clubs in South America.
"Carlos will not play for any other Brazilian club than Corinthians, that is an absolute certainty," he told ESPN Brasil.
"Boca Juniors and Corinthians are in his heart. He would only play for the these two clubs if he when back to Brazil and Argentina."
The Brazilian transfer window closes on July 20, which means any deal need to be done soon - but Joorabchian insists that Tevez does have other options in Europe.
"The priority is Corinthians, but we have other options," he said.
"Carlos was the best player in the Premier League [last season], he was the scorer of the team for two consecutive years, he won the FA Cup.
"So he has much appeal in the European market. He is no longer a boy, today he is a great player."
Joorabchian insists that playing in Brazil would not be a step down for Tevez, adding: "Football in Brazil has changed, grown. His dream was always to return to the Corinthians, and this time there is a possibility."
Tevez used to play for the Brazilian outfit before heading to West Ham five years ago - the start of a turbulent spell in England that has also involved two seasons at both Manchester clubs.
It is thought the massive transfer fee, almost treble the club record ?13.7million that got him to the club in 2005, would be funded through sponsorship and money from a new TV rights deal in Brazil.
If the full transfer fee materialises, it would surely prove attractive to City owner Sheikh Mansour.
City are currently in the United States for a three-match tour that forms part of their build-up to a new season. Some senior players have already expressed their dissatisfaction with Tevez's status as captain, requesting Vincent Kompany is handed the job instead.
Yet Tevez remains a key figure in the City line-up. His 20 Premier League goals last term secured him a share of the Golden Boot prize and, without the forward, manager Roberto Mancini would have to act fast to bring in reinforcements.
Atletico Madrid's Sergio Aguero has been mentioned as one such alternative, although he would probably cost just as much as City would receive for Tevez.
Source: Team Talk
Source: Team Talk