Jose Mourinho is a fan of the 29-year-old and is hopeful of taking advantage of the strained relationship the Brazil international has with the Blues' in limbo manager Antonio Conte, following his limited game time at Stamford Bridge last season.
Although Conte is expected to be forced out of the club this summer, with Maurizio Sarri expected to take the reigns, Willian's future remains uncertain and the Express claim the United boss is eager to make the most of the situation.
The report claims that Willian's age could make the Blues consider cashing in on the Brazilian if they were to receive and offer in excess of £50m, although they prefer not to sell to a direct rival - which comes as a boost to Barcelona.
Mourinho, however, is eager to start a bidding war to land the player who impressed during his Chelsea days and Willian could be tempted by the opportunity of a reunion with his former boss, particularly as uncertainty continues to surround who will be in charge at Stamford Bridge next season.
The lack of Champions League football with Chelsea next season could also come under consideration for Willian when considering offers made by both Barcelona and United.
Willian, who turns 30 in August, has played over 200 games for Chelsea since joining the club in 2013 and is currently with Brazil in Russia - where he featured in all of the World Cup group games as Tite's side secured their passage to the Last 16.