The report claims that, having signed Nemanja Matić from the Blues for £40million already this summer, United boss José Mourinho is keen to reunite with another member of his 2014/15 title-winning Chelsea side in the form of the Brazil international.
A fee of around £35million has been mooted for the 29-year-old, with the Premier League champions linked with a move for Leicester City's Riyad Mahrez.
The Football Whispers Index, which utilises a unique algorithm to give every transfer rumour a score out of five based on validity, rates United's chances of landing Willian at 2.0.
Mourinho is believed to have listed Willian among his transfer target for the wide attacking positions, and has made no secret of his desire to add a four new signings this summer, having already splashed £150million on Romelu Lukaku, Matić and Victor Lindelöf.
However, many reputable outlets, including BBC Sport, claim that the Old Trafford club are expecting a “quiet” deadline day, with a handful of young players being sent out on loan their only activity.
There is, of course, the possibility that United will spring into action if one of their top targets suddenly becomes available. And if, as is being reported in some quarters, Chelsea are confident of completing a deal for Mahrez, then Willian moving to the red side of Manchester is not completely beyond the realms of possibility.
But the discord within Chelsea caused by Matić's sale to United, in effect strengthening a direct rival, is likely to preclude any such deal being struck in the near future for Willian.
Stylistically, as a hard-working, productive and versatile attacker, Willian perfectly fits the bill for United, and Mourinho has spoken of wanting a player capable of playing wing-back, as Willian is, to enable him to use a back three at times.
But, especially at this late stage, a United move for Willian appears unlikely.