Real manager Zinedine Zidane has admitted that his club could be in the market for players during the January window and Luiz, who is also interesting Manchester United, has been discussed as a potential target.
Chelsea are expected to make another move for Juventus wing-back Alex Sandro, who is rated at £60m, in January, a player they failed to land in the summer.
Luiz had a massive fall out with Conte after the Champions League draw with Roma at Stamford Bridge, when the manager was unhappy with the Brazilian’s reaction after being substituted.
There were further problems between the pair following the 3-0 defeat in Rome, after which Conte conducted a heated dressing-room inquest.
Luiz trained alone and was dropped for the 1-0 win over United after apparently questioning Conte’s tactics and he also missed games against West Brom and Liverpool, though was recalled for the Champions League win over Qarabag last week.
Luiz will also miss the clash with struggling Swansea at Stamford Bridge tonight after Conte revealed he had suffered a knee injury and doubts remain over the 30-year-old’s future at Chelsea.
Conte said: “I must be honest, in this moment it’s very difficult for me to answer how long David Luiz will be out. It will be up to the doctor to assess the situation very well and then to take the best decision for the player.”
Chelsea though would not sell Luiz in January unless they could find a replacement, with Conte already concerned about the depth of his squad. The Brazilian has just over 18 months left on his contract, after returning to Chelsea from Paris Saint-Germain in the summer of 2016 in a £34million deal.
Conte made no secret of his unhappiness with Chelsea’s transfer dealing at that time and the club are expected to bring in at least one or two players in January.
Borussia Dortmund striker Pierre-Emerick Aubameyang is expected to be another target.
Chelsea go into Wednesday’s clash against Swansea unbeaten in their past five Premier League matches. And Swansea manager Paul Clement returns to the club where he was once a coach with a ringing endorsement of Alvaro Morata.
Clement, who worked with Morata at Real Madrid, had no doubts he would come good.
“He’s strong, quick and good in the air,” he said.