Luiz was a surprise omission from the Blues squad for the visit of Jose Mourinho's side, with Denmark international Andreas Christensen named from the start of the 1-0 victory at Stamford Bridge.
The Times understands the decision for Luiz – who sat in the stands behind the Chelsea bench for the duration of the 90 minutes – stems from a conversation with Conte on Thursday (2 November) in which he was perceived to have questioned the Italian's authority.
The exchange followed the 3-0 Champions League defeat to Roma. 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.
Conte then met with the entire Chelsea squad during which he lambasted their performance. Luiz's Brazilian teammate Kenedy was subsequently left out of the squad to face United after being caught yawning during the meeting.
Prior to being omitted from the 18-man squad on Sunday, Luiz was forced to train away from the first team and instead worked with the club's youth squad. Chelsea went on to win their fourth Premier League game in a row to go within a point of United in the table, but Luiz's future is now under the microscope.
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. Luiz could yet be next, despite his role in Chelsea winning the title last season.
Following the game, Conte denied any falling out with Luiz and hailed the impact made by Christiansen, who has made 12 appearances this campaign after returning from two seasons on loan at Borussia Monchengladbach.
"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. Today, I did this, and Christensen played an amazing game. I was very happy for this.
"It's very simple. The coach has to make the best decision for the team. Tonight, the best decision for the team was to play with Christensen and to have [Ethan] Ampadu on the bench, young players, really good players for the present and the future. Maybe in the future I can decide in a different way, or continue in this way. I must take the best decision for the club, not for a single player. Sometimes, I can make mistakes or sometimes I can do the best thing."