Luiz has started once since the 3-0 loss at Roma on October 31, having been dropped for the visit of Manchester United on November 5 amid talk of a fallout.
Since starting at Qarabag in the Champions League, the Brazil defender has been out with inflammation around his knee and Conte has previously bristled at suggestions of a breakdown in their relationship.
Asked about the issue again ahead of today’s Premier League visit of Southampton, Conte said he would like Chelsea medical director Paco Biosca to corroborate Luiz’s injury.
“I understand that someone is thinking that I’m not telling the truth. I’m disappointed about this, but I can understand it,” Conte said.
“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 will try to solve the situation. I think we can call the doctor and organise a (media) conference with the doctor for him to explain the medical situation.”
Luiz is continuing his rehabilitation, but returned to running on the pitches at Chelsea’s Surrey training base this week.
The 30-year-old, re-signed from Paris St Germain in August 2016, was an integral figure in Chelsea’s title win last season, but has recently been linked with a move amid suggestions he is unhappy.
Conte says all of Chelsea’s players should be happy.
“I understand that every player wants to play, this is normal. But we must be very, very, three, four, 1,000 times happy to have this job, to have this life,” Conte said.
The form of Andreas Christensen has led many to suggest Luiz will struggle to regain his place once he has recovered his fitness. Conte played that prospect down, due to the fixture schedule.
He added: “Until now, my players — every player — have all played a lot of games.
“We have to play every three days and it’s right to make rotations and give opportunities to every player.”
Conte says he is being realistic in suggesting his third-placed team are out of title contention. Manchester City have an 11-point lead over second-placed Manchester United and a 14-point advantage over Chelsea in third.
The Blues have dropped just four points in the last nine games, in the draw at Liverpool and loss at West Ham, as City have increased their lead.
Conte said: “When I speak, we must be realistic. In the last nine games we won seven games, drew one and lost one. And the distance, the gap, improved for Manchester City.
“Time is moving on. They are continuing to win.
“During the transfer market they reached their first targets and they created a great team,” he added.
Striker Alvaro Morata was Chelsea’s marquee signing last summer, as a direct replacement for Diego Costa, who left for Atletico Madrid.
Morata is available again after missing Tuesday’s win at Huddersfield with a back problem and due to fatigue. Defender David Luiz (knee) remains out.
Spain striker Morata, signed for an initial £58m from Real Madrid, told the in-club magazine this week that he has been watching footage of Didier Drogba, who scored 164 in 381 appearances across two spells.
“Two different players, different characteristics,” Conte said. “Didier Drogba, I think, he wrote the history of this club. He’s a wonderful player, a wonderful striker.
“I think he’s more powerful than Alvaro, but Alvaro, don’t forget, has a lot of space for improvement.
“He’s strong physically, is a technical player. I see a great future for Alvaro.”