The deal would make the German star one of the highest paid players in MLS history, as he continues to struggle at Old Trafford having been frozen out by Jose Mourinho.
Bastian Schweinsteiger has been offered an escape route out of Manchester United by Chicago Fire.
Goal understands that the MLS side have offered the midfielder a three-year deal worth $5.5 million per year.
Veljko Paunovic’s side have endured a disappointing MLS campaign, finishing bottom of the Eastern Conference, but they remain hopeful of persuading the former Germany international to make the move.
Paunovic met with Schweinsteiger earlier this month in Manchester and is optimistic he can land the 32-year-old in time for the start of pre-season training.
Schweinsteiger was signed for Manchester United by Louis van Gaal from Bayern Munich but failed to make much of an impact under the Dutch coach and his season was ended prematurely by injury.
However, he did manage to recover in time to feature at Euro 2016 for Germany, scoring in the win against Ukraine before retiring from international football after the tournament.
Schweinsteiger was subsequently completely frozen out at Old Trafford following the arrival of Jose Mourinho and has not made an appearance for the Red Devils all season after being deemed surplus to requirements by the Portuguese.
Despite being banished from first-team training the 32-year-old has frequently insisted he is ready for action if Mourinho were to call upon his services and that he is hopeful of being given a chance in the first team.
There does appear to have been a slight softening towards Schweinsteiger recently by Mourinho with the midfielder having been welcomed back to first-team training in October.
The Portuguese insisted it was a “human” decision to recall the midfielder while Schweinsteiger admitted it “felt great” to be back amongst the first-team and has insisted he will give his all in training in a bid to convince Mourinho of his worth.
However, despite his training return Mourinho appears no closer to selecting Schweinsteiger who is widely expected to leave the club when a suitable offer arrives.