The former Germany captain had 15 months left on his contract and United were willing to forgo a transfer fee for the 32-year-old, says the Daily Mail.
Schweinsteiger's switch to Major League Soccer is seen as a clean break by Jose Mourinho, who quickly decided that the midfielder was surplus to requirements.
Struggling Chicago Fire requested that the deal was done now rather than in the summer and Mourinho sanctioned that, given Schweinsteiger was set to play no part in the run-in.
Schweinsteiger, who had already moved out of his house in Hale, wants more games and signed terms on a one-year stay. He could have asked United to pay a lump sum in line with his three-year contract. That might have risen to around £10million.