This is according to The Daily Mail, who suggest that the player is ready to leave the Blues this summer after three-years in the Premier League.
The same source further states that while Barcelona - who themselves have been strongly linked with a move for the maverick centre-back in recent weeks - is reported to be Luiz's favoured destination, there appear to be doubts at the Nou Camp as to whether he is an ideal purchase at this time.
Former Barca boss Pep Guardiola appears to be very interested, however, with Bayern Munich's quite shocking defeat to Real Madrid in the second-leg of their Champions League tie last month suggesting that they could perhaps require a touch of defensive strengthening prior to the start of the 2014/15 campaign.
A composed and largely versatile player who is certainly not afraid to carry the ball forward, Luiz has mostly impressed during his time at Stamford Bridge.
However, despite this, questions over a potential lack of reliability have always lingered and it seems that Luiz has fallen significantly behind the likes of English duo Gary Cahill and John Terry in Chelsea's defensive pecking order under Jose Mourinho.
Just when Bayern Munich plan to launch that aforementioned bid remains to be seen and it will be intriguing to see if they opt to move before or after the 27-year-old returns to his native Brazil for the World Cup.
While it appears at the moment that Chelsea are willing to part with Luiz, a strong showing at the tournament as part of Luiz Felipe Scolari's squad could surely test that resolve.
An impressive World Cup campaign could also see Luiz's price tag rise sharply, so it may well be in Bayern Munich's best interests to try and complete a deal prior to the summer.