Bayern Munich tabled a series of bids for the youngster in January, all of which were rejected by the Blues.
But Hudson-Odoi has not extended his contract at Stamford Bridge and The Daily Mail are reporting that United have now entered the race.
The winger’s current contract expires at the end of next season, with no further substantial talks having taken place since January.
United have also been linked with fellow England international Jadon Sancho who represents Bundesliga outfit Borussia Dortmund.
And Red Devils fans are less than convinced by Hudson-Odoi’s potential and would seemingly prefer their club focused on bringing Sancho to Old Trafford.
One fan tweeted: “Come on guys the guy can’t even break in Chelsea first team and this is the person we want to buy? That would be a waste of time.”
“Sancho is miles ahead,” wrote another. “The guy has the second most assists in Europe and has made his champions league debut.
“CHO hasn’t even started in the league yet.
“United are losing the plot a bit,” added a third. “They should be buying a few more proven players than the people the English media hype for this or that reason.
“This doesn’t mean that one of them won’t grow up to be the best, but United have too many potential “great” players.”
Reports linking Hudson-Odoi with a move to Man Utd come amid news of:
Hudson-Odoi was “speechless” after becoming the youngest player to represent England in a competitive international during Friday’s 5-0 hammering of the Czech Republic.
“I’m absolutely delighted,” the 18-year-old told ITV. “I just want to thank everyone who’s helped me get where I am today.”
Arsenal legend Ian Wright cannot understand why Hudson-Odoi is still being marginalised at Chelsea by manager Maurizio Sarri.
“I think when we watched him in the Under-17s when they won the World Cup, he was one of the outstanding players,” he told ITV .
“I think that listening to Gareth Southgate about he’s ready and how impressive he’s been and he’s got no problem bringing him in, he looks like an international, I thought: ‘That’s a message, that’s a message back saying how is this guy not playing?’.
“A message back to Chelsea, a message back to the manager of Chelsea. You look at him and he’s ready to go. Bayern Munich are showing that he’s ready to go. Why isn’t he playing?”