The Brazilian defender has made just one appearance for Chelsea since October 31, when he played the entirety of the club's 3-0 Champions League defeat against Roma at the Stadio Olimpico.
He was subsequently dropped from Conte's squad for Chelsea's home clash with Manchester United after the 30-year-old is believed to have questioned the Italian's tactics.
Luiz then made the bench for Chelsea's away game with West Brom, but was an unused substitute at the Hawthorns, though he started against Qarabag in the Champions League the following week.
However, after again being left on the bench for Chelsea's clash with Liverpool, Luiz suffered inflammation in his right knee and has since been sidelined with the issue.
Standard Sport understands the injury is real, with Conte having insisted the same on several occasions although Chelsea have not put a timeframe on the defender's return from the issue.
Luiz was seen doing individual work with the Chelsea physios at Cobham on Friday for the first time since sustaining the knee injury, although Chelsea's game at home to Southampton on Saturday will still come too early for the 30-year-old.
But after being questioned about his relationship with Luiz and whether the Brazilian's injury is genuine, Conte suggested holding a press conference with the club doctor to prove he isn't lying about the defender.
"To stop this, I think it's right to call the doctor and to have a conference with him," Conte told reporters.
"I think this is a good idea. I understand that someone is thinking that I'm not telling the truth. I'm disappointed about this, but I can understand it.
"I'm disappointed because I like to tell you the truth at every moment. I'd like to tell you a bad truth rather than a good lie.
"I think we can call the doctor and organise a conference with the doctor for him to explain the medical situation of all my players and, in this way, I can avoid having to answer this question. Avoid the creation of this atmosphere of 'it's not true what he's telling us'.
"I am disappointed about this, but I will try to solve the situation."