The newspaper claims that Hudson-Odoi, 18, is on the wishlist of manager Ole Gunnar Solskjaer, who also wants to sign Declan Rice from West Ham in the summer transfer window.
It is understood that Hudson-Odoi has 14 months remaining on his current contract at Chelsea.
The England international made his first Premier League start for the London club on Wednesday night as they won 3-0 against Brighton.
Good move for Manchester United?
Hudson-Odoi would be a terrific signing for Man United and Solskjaer should definitely push out the boat to sign the teenage sensation in the summer transfer window.
He has struggled to play regularly for Chelsea this season, but that seems to be more down to bad management by Maurizio Sarri than being anything to do with the attacker’s quality.
The two-times England international has massive potential and could be one of the Premier League’s best players if he is handed regular first team football in the next few years.
Man United would also deal a serious blow to one of their top-six rivals if they did snatch Hudson-Odoi from Chelsea.
This is Futbol rating 10/10
Likely to happen?
Hudson-Odoi is bound to be wanted by a lot of clubs in the summer, and the teenager could yet pen a new deal at Stamford Bridge.
If he does stay in England then Man United would be a likely destination for him, but Chelsea might not want to do business with one of their rivals, even if the forward is in the final year of his contract.
This is Futbol rating 3/10