Schweinsteiger has been training with the reserve side and not played a single pre-season game for United.
The Germany international has been told he can leave the club and he has had no shortage of suitors.
The experienced midfielder’s former club Bayern Munich have become the latest club to offer a lifeline.
Bayern CEO Karl-Heinz Rummenigge said they would be open to discuss the possibility of Schweinsteiger returning to the club.
“Should he [Schweinsteiger] speak in the future at some point about a desire to return, then we will discuss it with him,” Rummenigge told Bild .
Former teamamte Lahm meanwhile said he would be happy to have Schweinsteiger back at the club.
“It’s important to bind players who deserve it to the club,” Lahm said. “Basti knows everyone and everything here, he would be predestined to work in the team.”
The Istanbul giants will compete in the European football competition this season and are keen on strengthening their midfield.