The Brazil international was a surprise omission from the Blues squad for the visit of the 20-time champions of England two weeks ago, with Denmark international Andreas Christensen named from the start of the 1-0 victory at Stamford Bridge.
Chelsea boss Antonio Conte's stemmed from an exchange with Luiz in which perceived his authority had been questioned following the Blues' 3-0 defeat against Roma in the Champions League three days earlier.
Though Luiz was part of the defence mercilessly taken apart by the Serie A side, he felt he was unfairly singled out by the Chelsea coach for his role in the reverse and was subsequently order to train with the youth team, while the senior squad prepared for United's visit.
Luiz is understood to be unhappy about his treatment and, according to the Daily Express, Mourinho is monitoring the situation and could even table an offer as early as in the January transfer window.
Should the United manager move for the Chelsea defender, it would mark a dramatic shift in the relationship between the pair, which has been frosty in the past.
The Portuguese coach only worked with Luiz in the 2013-14 campaign, his first season of his second spell at Chelsea. However, the ex-Benfica man only started 15 games, most of them in midfield, as John Terry and Gary Cahill formed Mourinho's preferred centre-back pairing, while Luiz was sold to Paris Saint-Germain in the summer for a then world-record £50m fee for a defender.
Following the Brazilian's departure, Mourinho suggested he "would not be missed", only for the former to retort the Portuguese manager was not "special", after PSG knocked Chelsea out of the Champions League in the 2014-15 campaign.
However, the rapport between the duo appears to have improved and Mourinho is understood to have been impressed with Luiz's performances since the defender returned to Stamford Bridge at the beginning of last season.
Following Luiz's omission from the starting XI against United, Conte sought to minimise speculation about a rift between him and the player suggesting his decision had been merely tactical.
"It was only a tactical decision," he insisted. "This can happen to any one of my players. If I see they are not in good form, it's normal. I have to put my face in every situation, and sometimes make important decisions.
"It's very simple. The coach has to make the best decision for the team."
Though it remains to be seen how the incident impacts on Luiz's future opportunities, the likes of Diego Costa and Nemanja Matic have seen confrontations with Conte lead to their eventual departures.