The Sunday Mirror says United, who paid Media Sports Investments an initial £6m to take Tevez on a two-year loan deal, are unwilling to spend the £28m it will cost to secure the 24-year-old on a permanent basis.
But Tevez's agent, Kia Joorabchian, has already been alerted to widespread interest in the striker both at home and abroad.
A source close to Joorabchian said: "Kia is very relaxed about the whole Tevez situation because he knows if United don't want to do a deal, some of the world's biggest clubs will want to do business.
"But the situation is that Carlos is very happy at United and that is the club he wants to play for."
However, much will depend on how many games Tevez plays this season.