According to Tony Banks in the Daily Express, the Portuguese could move for his former player as early as January and Luiz could be open to the switch as he is "angry" about his recent treatment at Chelsea.
Luiz, 30, was dropped for the Blues' last game before the international break—the 1-0 home win against United—and his replacement, Andreas Christensen, enjoyed an impressive performance.
After the match, manager Antonio Conte was asked about Luiz's future at the club and he said, per the Guardian's Dominic Fifield: "I don't know. He has to work really hard, otherwise they are on the bench or in the stand."
It subsequently emerged Luiz had been dropped for questioning Conte's tactics in the wake of the 3-0 defeat to AS Roma and ended up training away from the senior squad, per Matt Hughes in The Times.
Luiz returned to Chelsea ahead of last season after two terms with Paris Saint-Germain and was excellent as part of Conte's back three, which played such a key role in the Blues winning the Premier League.
He was included in the PFA Premier League Team of the Year, alongside team-mates Gary Cahill, N'Golo Kante and Eden Hazard:
#PFAawards | The PFA Premier League Team of the Year sponsored by @OfficialPanini https://t.co/eQfXZ6h5Ll2017-4-20 07:59:47
However, Luiz's form in 2017-18 has been poor and his first-team future at Stamford Bridge looks in serious doubt, especially if Christensen continues to impress.
There could be a place for him at United, though, where back-up centre-backs Chris Smalling and Victor Lindelof are failing to impress on a consistent basis.
First-choice duo Eric Bailly and Phil Jones have been largely fantastic so far this term, but the Englishman in particular is quite injury-prone.
Mourinho may then see the benefit of bringing in a player of Luiz's experience and personality if he believes he can get him back to his best form again.