A report from French source RMC Sport (h/t Callum Vurley of the Daily Star) has noted how Luiz is determined to quit the Blues for La Liga giants Real. The issues stems from Luiz being dropped by Chelsea manager Antonio Conte in favour of Andreas Christensen.
Luiz has missed Chelsea's last two Premier League games, and Vurley also detailed how Conte remained uncertain about the Brazil international defender's availability for the Blues' upcoming league game at home to Swansea City on Wednesday.
It seems much more likely Chelsea would look to offload Luiz to a team outside England's top flight, though. Conte followed a similar approach when he fell out with striker Diego Costa last season.
The argument was settled by Costa being allowed to rejoin old club Atletico Madrid and wait to be eligible to play for Los Rojiblancos this January. Sending Luiz to La Liga would be a great way for Conte to settle another testy dispute.
Chelsea are well-positioned to part ways with Luiz, even though Conte still plays three at the back. Signing Antonio Rudiger from Roma this summer helped improve Chelsea's depth at centre-back, but the emergence of Christensen has proved decisive.
The Denmark international returned to Stamford Bridge after several loan spells and has looked comfortable starting for the Blues this season. In fact, Christensen recently became the first academy graduate since John Terry to start three league matches in a row, according to Anthony Chapman of The Sun.
Still just 21, Christensen has given Chelsea a burgeoning young star at the back. He's joined incumbents Gary Cahill and the outstanding Cesar Azpilicueta to improve the Blues' three-man back line.
Luiz has always been comfortable on the ball and a danger from set pieces. However, the 30-year-old remains suspect defensively.
If Chelsea can cash in on Luiz this winter, it would solve a big problem for Conte while giving him the funds to bolster other areas of his squad for the season's run-in.