There was no immediate confirmation from either club or the Swedish striker's management.
The 36-year-old has been linked for some time with a move to the United States and Major League Soccer. Los Angeles Times writer Kevin Baxter said on Twitter that Ibrahimovic had signed for LA Galaxy.
The BBC said it was understood United manager Jose Mourinho had agreed to release him from a contract that was due to expire at the end of June.
Mourinho said at the beginning of March that Ibrahimovic was expected to leave at the end of the season.
Sweden's record international goal-scorer with 62 strikes in 116 games, Ibrahimovic told Reuters on March 15 he was finally over a serious knee injury that stalled his United career.
Having sustained a bad knee injury in United's Europa League quarter-final against Belgian side Anderlecht in April, 2017, Ibrahimovic last appeared for the Premier League club on Dec. 26 against Burnley.
(Reporting by Alan Baldwin, editing by Toby Davis)