Manchester United are thought to be interested in a potential deal to sign the Brazil international in the 2018 summer transfer window.
Willian was used sparingly towards the end of the season under Blues manager Antonio Conte to fuel speculation surrounding his future.
The South American forward hit out at Conte on Instagram following his omission from the Chelsea FC starting line up in the FA Cup final.
Mourinho has been linked with a move to sign Willian since the Portuguese head coach took over the reins in May 2016.
Sky Sports News reporter Graves shed light on why Mourinho is keen to sign Willian to bolster his squad ahead of the new season.
“Mourinho knows he can trust him,” Graves told the Transfer Talk podcast.
“He has worked with him before. Maybe Mourinho has learned his lesson. He wants to work with players whose character he knows.”
Manchester United have signed Brazil international Fred in a £52m deal from Ukrainian Premier League champions Shakhtar Donetsk.
The Red Devils have also spent £17m on Portuguese defender Diogo Dalot from FC Porto to bolster Mourinho’s defensive options, as well as goalkeeper Lee Grant.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news