The Portuguese is a huge fan of Willian, who was arguably the only stand-out performer during Mourinho’s dismal final season at Stamford Bridge, scoring seven times before he was sacked in December last year.
However, the Brazilian has dropped down the pecking order under new manager Antonio Conte since he shifted to a 3-4-3 formation.
Conte has preferred a front three of Eden Hazard, Diego Costa and Pedro while Victor Moses, who was frozen out by Mourinho, has impressed on the right side of the midfield four.
And, according to the Daily Star, Mourinho is keen to take advantage of this by bringing the £40m-rated star to Old Trafford to add some pace to his attack.
Willian, who won the Blues’ Player of the Year last season, has not started a game since the 2-0 win over Hull on October 1, with injuries and a family bereavement limiting his chances since then.
However, he was not even included in the squad for last Sunday’s 1-0 victory over Middlesbrough at the Riverside after returning from South America on international duty.
United have hope they can persuade Chelsea to sell in January having successfully done so with Juan Mata in 2014, albeit £37.1m.