Hudson-Odoi, who has also attracted interest from Borussia Dortmund, will have just a year remaining on his contract with Chelsea at the end of the season.
But manager Maurizio Sarri will face uproar from supporters if he allows the academy graduate to leave Stamford Bridge on his watch.
"The second problem is Hudson-Odoi, it is not a very serious problem but I don't know if he will be able to play in the next match".
Hudson-Odoi's appearance as a substitute at Watford on Boxing Day is his only Premier League outing since Sarri took over as Chelsea boss during the summer.
Pogba leads resurgent Man United to win over Bournemouth
Manchester United ended the year on a high, as they beat Bournemouth 4-1 at Old Trafford on Sunday afternoon. His two goals aside, his movement and passing repeatedly caused Bournemouth problems.
He's certainly not the finished article yet, but he's got electric speed and has shown he can go past full-backs easily.
Kristof Terreur of Het Laatste Nieuws claims that Bayern are prepared to follow Bundesliga rivals Borussia Dortmund in the race for the 18-year-old.
The U-17 World Cup victor has featured in just six games in all competitions this season, with his only appearance in the Premier League coming against Watford on Boxing Day.
Chelsea are looking to win three consecutive Premier League away games for the first time under Maurizio Sarri, last doing so in April when Antonio Conte was in charge.
Though Hudson-Odoi apparently recognises that his talents are highly regarded in west London, the winger is said to be keen on getting more regular first team action.