The 36-year-old still has six months left on his existing deal at Old Trafford, signed as he continued his rehabilitation from the knee injury that ended his first year at United.
However, Galaxy refused to be drawn into discussion over the proposed move and are yet to make any official announcement, although the deal is still expected to be pushed through before tonight's transfer deadline.
Zlatan Ibrahimović could be heading to the United States after his stint with Manchester United.
The striker has scored just one goal this season, in the EFL Cup.
Jose Mourinho has admitted that the club will allow the Swedish forward to leave the club this month, but made it clear that the final decision rests with Ibrahimovic. "But if it is true and Zlatan wants a future in another club in another country then we are here to help and create conditions for that to happen, not to make his life hard".
Speaking to the press, Manchester United manager Jose Mourinho commented on the Ibrahimovic to LA Galaxy situation by saying: "If it is true and he wants a future at another club we are here to help". We will not make his life hard.More news: Match-Fixing? 5 Stumpings, 3 Runouts In One Innings
More news: President Buhari arrives Addis Ababa for AU meeting
More news: In security update, Apple backports Meltdown fix to older macOS versions
"He's working hard to be fit".
"He's a very important player for me and a great professional who is giving everything he can to help the team", said Mourinho.
The 116-cap former Sweden global striker joined Man Utd in 2016 after his contract with French giants Paris Saint-Germain expired.
Ibrahimović has been linked to a move to Major League Soccer (MLS) for some time now, but he never made the switch.