The veteran midfielder has been frozen out by Jose Mourinho and is believed to be on the hunt for a new club.
"I think America is great. Moving abroad is good for personality development and it would also be good for our children," Galatasaray's Podolski told Bild.
"Clearly it would be possible to play with Schweinsteiger in the States. What happened to (Schweinsteiger) is unfair.
"It is not correct to deport Basti to the second team. A coach must always keep the doors open to all players."