The Red Devils have been regularly linked with a move to sign the Brazil international in the lead up to the 2018 summer transfer window.
Manchester United finished in second place and three spots above the Blues in the Premier League table to secure Champions League football.
The 20-time English champions lost 1-0 to Chelsea FC in the FA Cup final at Wembley after Eden Hazard’s first-half winner.
Willian came off the bench in the final minutes of the FA Cup showpiece to cast doubt on his long-term future at Stamford Bridge.
Sky Sports News reporter Graves believes Manchester United are genuinely interested in a potential deal to sign Willian from Chelsea FC.
“There is an interest from Man United in bringing Willian to Old Trafford,” Graves told the Transfer Talk podcast.
“It would be a sensational move. We think he would like to leave Chelsea if Conte remains the manager at Chelsea.”
Manchester United completed a surprise £40m deal to sign Serbia international Nemanja Matic from Chelsea FC last summer.
The Blues were heavily criticised for their decision to sell two-time Premier League winner Matic to Manchester United in 2017.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news