The 29-year-old has started just 14 games for the Blues in the Premier League this term, sparking rumours that he could be on his way out of Stamford Bridge.
United and AC Milan are 7/4 joint favourites to sign Willian who is contracted to Chelsea until 2020.
Red Devils’ boss Jose Mourinho is a known admirer of the Brazilian and was full of praise for his performance against United last Sunday.
Speaking after the his side’s 2-0 victory he insisted that Willian “will do great things in Russia” this summer.