The Brazilian international is thought to be edging ever closer to the Stamford Bridge exit door, with Jose Mourinho having grown frustrated with his unorthodox playing style.
Although technically adept, Luiz has shown himself to be prone to errors due to his adventurous approach to the game – which can leave his fellow defenders exposed.
Despite having rejected approaches from Barcelona over the summer, ‘The Special One’ is thought to be ready to let the 26-year-old leave if an acceptable offer is received.
This has alerted Bayern, with manager Pep Guardiola thought to be a fan of the South American star.
The Champions League and Bundesliga champions are believed to be in the market for reinforcements as they set about establishing themselves as European football’s dominant club force.
Luiz has made only 11 appearances this term under Mourinho, which could be a concern for him in the build-up to the 2014 World Cup.
A big move to Bayern may allow him a fresh start and the chance to play regularly ahead of the showpiece tournament in his homeland.
However, a deal may hinge on Chelsea signing a new centre-back, with only Branislav Ivanovic – often used on the right side of the backline – as cover for John Terry and Gary Cahill if Luiz were to leave.