The Daily Mail says City have received a remarkable £37million offer for Tevez from his former club Corinthians.
With the Brazilian transfer deadline in 10 days, they hope to force through a deal that will take the Argentina striker back to South America.
It is understood that Corinthians, who bring in £50m every year from their TV rights and £23m from main shirt sponsors Neo Quimica, can also satisfy the 27-year-old star's high wage demands.
Tevez has expressed a strong desire to leave Eastlands, citing a desperate need to live closer to his children. A return to Brazil would be attractive and the striker is now keen to see the clubs agree a fee.