He struggled for game time in the Portuguese's first season at the club, but looked like he was returning to form in Mourinho's second season, only to be resigned back to the bench following the arrival of Alexis Sanchez from Arsenal.
Nonetheless, Willian is being targeted by Mourinho with the two having a history of working together during their time with the Blues for a few years.
Willian, who scored double figures in all competitions for the third straight campaign, reportedly attracted enquiries from United back in January although were knocked back.
Under manager Antonio Conte, Willian has found his role more limited than previously, and it would not be a huge surprise were he to be open to a move away from Stamford Bridge.
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"He can improve (them) a lot".
Maddison was looking to stay in the Midlands region where he grew up and hence chose to join the 2015/16 Premier League champions.
The Chelsea attacker is under contract in London until 2020 and recently hinted that he would be interested in an Old Trafford switch as he hailed compatriot Fred's move to "one of the best teams in the world".
"I think he has gone to a club like Man United and he's got players that have come through the youth from a club that predominantly continues to bring through youth players".
The ex-Bournemouth loanee, however, is said to be unhappy with Emery's desire to utilise him as a squad player and not as a regular starter in his team. "We talked a little bit about that".