The pair were thought to be involved in a heated altercation follownig the Champions League loss to Roma in October, with Luiz yet to feature in the Premier League since.
Youngster Andreas Christensen appears to have leapfrogged Luiz in the pecking order at Stamford Bridge, though Conte insists that the former PSG man is currently sidelined with a knee injury, nothing more.
Speaking on 'Sunday Supplement', Sunday People Chief Football Writer Steve Bates has gone on the record saying that he believes that Luiz will be on the move come January.
"At his (Conte's) press conference on Friday he was at pains to point out that this knee injury is genuine," said Bates. "I had no reason to believe it's not.
"I think his problems at Stamford Bridge go deeper than just a knee injury. From the start of the season there's not been an easy relationship with Conte. He's a very demanding, highly-strung boss. Obviously, in the summer we saw David Luiz's big pal Diego Costa shipped out of the club as well."
Bates believes that Christensen's impressive performances, coupled with his tender years make him a prime candidate to represent Chelsea for years to come, something which pushes Luiz closer to the exit door.
"The pair of them (Conte and Luiz) clashed after the Roma defeat in the Champions League and I don't think the situation has repaired itself. Andreas Christensen is playing extremely well at the heart of Chelsea's defence. Conte probably sees him as the future. I don't think Luiz is going to sit around and maybe not be a regular or not be first choice having been at the club so long," he explained.
"I know for sure that Juventus would really, really like him. Whether that deal gets done in January I'm not sure, because they're still in the Champions League, but I suspect Luiz is not a long-term stayer at Stamford Bridge."