Luiz had a falling out with Chelsea booss Antonio Conte over tactics before the international break that cluminated in him being dropped for the visit of United a fortnight ago.
English publication 'The Express' reports that the anger from the fall-out has festered meaning that even after two weeks, there is still considerable bad blood between the pair.
That has left the 30-year-old considering his future and Mourinho, who previously worked with the player when in charge of the 'Blues' is considering a reunion.
That comes as something of a susprise, with Luiz and Mourinho hardly as thick as thieves during their season together. Luiz started just 15 Premier League games during the 2013/14 season, most of which came in midfield, with the Portuguese opting to go with Gary Cahill and John Terry at centre-back,
As if that weren't enough, after agreeing to sell the defender to PSG, Mourinho said that he 'would not be missed'.
However, it appears that all that has been forgotten, with Mourinho thought to have been impressed with Luiz's displays since rejoining the Premier League Champions from PSG last summer.
The aformentioned source claims thar United could look to do a deal as early as January.
Should Mourinho pursue a deal, it would certainly be bad news for Victor Lindelof, who has largely failed to impress since his summer move from Benfica.