The Brazilian was benched for the FA Cup final win on Saturday, the fourth time in five games that he has been omitted from the Chelsea starting lineup, with reports suggesting he will seek a move away from the club if Antonio Conte remains as manager.
Willian has two years left on his contract in the capital and hinted at a rift with Conte after editing the Italian out of a photo of Chelsea's trophy celebrations.
Manchester United boss Jose Mourinho is known to be a huge fan of the 29-year-old, having worked with him during his time in charge at Stamford Bridge and is reportedly keen to revisist a potential deal.
United are keen to strengthen their squad as they look to close the gap on noisy neighbours Manchester City, with a complete overhaul planned.
Willian has scored 44 goals in 236 games for the club since joining from Anzhi Makhachkala in 2013.