The Brazil winger revealed this week Jose Mourinho recently made an offer to take him to Old Trafford, but he remained at Stamford Bridge.
Willian was Chelsea's star performer under Mourinho last season before the Portuguese coach was sacked.
And according to the Daily Star, United will test the water over a move in the next transfer window.
Jose Mourinho tried to sign Willian at Manchester United in the summer but he stayed at Chelsea
Willian's been limited to making an impact from the bench, which he also admitted is far from ideal
A positive for the Red Devils is Willian has struggled to nail down a starting role this term.
Antonio Conte has opted for in-form Pedro and Eden Hazard as his wide attackers in recent months.
As a result, Willian's been limited to making an impact from the bench, which he also admitted is far from ideal.
Antonio Conte v Jose Mourinho: Chelsea managers' stats compared
Fri, December 16, 2016
Express Sport compares Antonio Conte's impressive start as Chelsea boss to Jose Mourinho's 2015/16 statistics
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Express Sport looks at how Chelsea manager Antonio Conte compares with his predecessor Jose Mourinho, 12 months after ‘The Special One’ was sacked at Stamford Bridge
But while they will be reluctant to sell last season's player of the year at the Bridge, a figure of around £40million is expected to encourage talks.
If Willian continues to appear largely as a substitute too, he could find leaving for Manchester more appealing.