Schweinsteiger is understood to have held talks with a number of MLS sides and would prefer a transfer to a major north American city such as Los Angeles or New York.
The 32-year-old returned to first-team training at United last month having been frozen out of the squad by Jose Mourinho, but the Portuguese manager has no intention of selecting him again.
United have attempted to negotiate an agreement with the midfielder to cancel his £150,000-a-week contract – which runs until 2018 – but the German wants the deal paid up in full.
If Schweinsteiger can agree a pay-off, he could join a new club for free in the January transfer window and would be willing to accept a reduction in his current salary. He is expected to become the first of a number of players to leave Old Trafford in the new year, with the likes of Timothy Fosu-Mensah – on loan – and misfit Memphis Depay expected to depart.
Mourinho’s decision to freeze out Schweinsteiger in the summer is understood have been influenced to some extent by senior figures at the club who became concerned with feedback about the World Cup winner last season.
Schweinsteiger was criticised for being unfit under Louis van Gaal and frustrated team-mates with constant trips back to Germany and to watch his tennis-star wife Ana Ivanovic.
Even this week, Schweinsteiger used time off on Monday to spend the day with Ivanovic in London and the former Bayern Munich man has never settled in Manchester.
Schweinsteiger is keen to avoid finding himself in a similar position at his next club and released a statement in August saying United “will be my last club in Europe”.
He joined United in 2015 for £8m but made only 18 Premier League appearances last season as he struggled with knee problems.
Mourinho believes Schweinsteiger lacks the mobility to feature for him and the World Cup winner is behind the likes of Paul Pogba, Marouane Fellaini, Michael Carrick, Ander Herrera and Morgan Schneiderlin in the pecking order at Old Trafford.