The paper reports that Bayern boss Pep Guardiola is a fan of the Brazilian and will look to land him at the end of the season, where Chelsea may be more inclined to sell up.
The former Barcelona boss is said to favour his ability to bring the ball out from the back, and sees him as an ideal addition to his squad.
The Brazilian joined the Blues in 2011 - but has had an up and down career in west London to date.
The former Benfica man was criticised for a string of errors soon after his move to Stamford Bridge, while last summer he was linked with a move away from the club following the arrival of Jose Mourinho.
Luiz has spent part of this season playing in an unfamiliar midfield role, amidst reports that Mourinho does not trust him at the back and prefers a central defensive partnership of John Terry and Gary Cahill.
Barcelona were heavily linked with a move for the Chelsea ace in the summer window, and reports today suggest the Catalan giants have made another enquiry over his availability.
Luiz is contracted to Chelsea until 2017 so won't come cheap for either Bayern or Barcelona - Bild say his current club will demand €29 million for the move to happen.
The paper adds that his exit from Chelsea is far from certain either, with Mourinho still yet to make his final decision on the player.
Barcelona look chronically short of options at centre-back and were linked with a host of defenders in the summer window.
It is likely that they will look to take a new defender to the Nou Camp in the winter window.