Willian has arguably been Chelsea’s best player this season and enjoyed some fine form in recent weeks.
Despite his good run, Blues boss Antonio Conte has used the Brazilian in fits and starts this term.
As a result, the 29-year-old has been consistently linked with a Stamford Bridge exit at the end of the season with United known to be big fans.
Bookmakers Ladbrokes says United have now been joined by Italian giants AC Milan in the race to land the winger.
Milan are currently priced at 7/4 shots alongside the Red Devils at the head of the market.
Alex Apati of Ladbrokes told Starsport: "Chelsea's season could be about to go from bad to worse as Willian looks set to be the next blockbuster name to leave Stamford Bridge, with Milan shock joint-favorites to strike a deal."
Ladbrokes also believe that Real Madrid, Barcelona and Paris St-Germain are in the running to secure Willian’s signature.
While it's looking increasingly likely that this season will be Willian’s last at Chelsea, Conte recently defended his treatment of the ex-Shakhtar Donetsk ace.
He said: “You think that I am stupid? When I put Willy on the bench?
“I have to try and make the best decision for the team, no? Maybe last season we won the title, or did I forget something?
“Now he is playing because he deserves to play. But not because there is some regret from the past. For what?
“If a player deserves to play, and shows me during the training session that he is on top of his form, and wants to work defensively, he plays.
“If not, stay on the bench, stay in the stands. But this is not only for one player but for all my players. This is what a winning mentality is.”
Willian netted Chelsea’s opener against United on Sunday but couldn’t help them avoid a 2-1 defeat at Old Trafford.
The Blues take on Premier League leaders Manchester City at the Etihad this weekend.