The Swede faces eight months on the sidelines due to knee injury and his United career is likely to be over.
Schweinsteiger says his ex-United teammate should move to the US.
He told Sport1: "Definitely. Players like him are really very important in a league like MLS. He is a very professional athlete and really gives you a lot of quality on the pitch.
"He may be (a little eccentric) and sometimes I think he over does it, but as a football player he is really one of the best I played with. He has a real, really good eye and he impresses me."