The Brazilian is believed to have fallen out with boss Antonio Conte.
He has not played in the Premier League since the victory at Bournemouth in October and now appears to be heading for the Stamford Bridge exit door.
He is not short of interested parties, with Juventus regarded the front-runners for the 30-year-old defender.
But Real Madrid are also keen on landing the star.
Luiz and Conte's relationship deteriorated after the 3-0 Champions League defeat to Roma on Tuesday, October 31.