That would allow the west London giants to secure a profit of £23m, having paid £30m to snap him up five years ago.
Barcelona may now be priced out of a move with Willian only wanted to provide competition for Ousmane Dembele, Philippe Coutinho and Lionel Messi.
United, however, have the financial muscle to make a transfer happen.
The Red Devils feel they can sign Willian having previously negotiated with Chelsea for deals involving Juan Mata and Nemanja Matic.
But Transfermarketweb say Willian could yet stay at Stamford Bridge.
New boss Maurizio Sarri, who replaced Antonio Conte last week, may choose to keep the player.
Chelsea transfer news: Maurizio Sarri may cost Man Utd and Barcelona the signature of Willian (Image: GETTY)
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The former Napoli manager usually sets his teams up with two storming wingers.
And Willian, therefore, could be deemed too important to sell.
Speaking back in April, before talk of a move to United or Barcelona surfaced, the Brazilian expressed a desire to stay at Chelsea.
“I think we have to continue to improve for next season,” he said.
“To improve ourselves. To think about what we did well, what we did not so well and to try to make something different next season.”