Luiz’s future had been in doubt after he was dropped for the clash with Manchester United earlier this month.
After the 1-0 win, Conte said he was unsure if the Brazil defender had a future at the club.
He said: “He has to work really hard otherwise they are on the bench or in the stand.”
Since then Luiz has made just one appearance for Chelsea, against Qarabag in Champions League, with Andreas Christensen taking his place in the starting XI.
And it appears Luiz is preparing for an exit by speaking to Madrid.
According to French outlet RMC Sport, Luiz has held discussions with the Champions League holders over a possible January transfer.
Luiz is not eligible to play for Madrid in the Champions League but that is not viewed as an obstruction to the transfer being finalised.
Should Luiz leave Chelsea, it would be the second time he has left the club having departed in 2014 and joined Paris Saint Germain.
Chelsea face Swansea in the Premier League on Wednesday and Luiz looks set to miss the match with a knee problem.
Manager Antonio Conte said: “I must be honest at the moment it is difficult for me to answer [how long he will be out].
“It will be up to the doctor to assess it and take the best decision.
“I don’t know [how long].”