The Germany international has been at the club since 2002, and has gone on to make 500 senior appearances in total.
However, injury restricted Schweinsteiger to just 28 appearances under Pep Guardiola last season, with Xabi Alonso taking responsibility in the heart of midfield.
And World Cup winner Lothar Matthaus believes the 30-year-old should swap the Allianz Arena for Old Trafford in order to save his career, telling SportBild: "I can understand that Schweinsteiger is wondering about his future.
"Bastian announced that he wants to play football on the highest level until 2018. But in the way he was used at Bayern recently, I think this is impossible.
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Bastian Schweinsteiger has had limited pitch time under Pep Guardiola at Bayern Munich
"Schweinsteiger needs a coach who fully trusts him and will tune the system around him. If Schweinsteiger gets an offer from a top European club, I would advise him a transfer in the summer.
"If the rumours are true that Louis van Gaal wants to bring him to Manchester United, Schweinsteiger should think about that carefully. If Van Gaal wants him, he will let him play where his strengths are."
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