The Brazilian centre-back’s future at Stamford Bridge is currently the subject of much doubt, with Blues chief Jose Mourinho believed to be willing to axe him with Kurt Zouma heading to the club as backup for solid first choice pairing John Terry and Gary Cahill.
Luiz has often been criticised for lapses in concentration, but is still a key player for Brazil – who he will represent at the World Cup – and is wanted by Barcelona.
Now Bayern are ready to step up their interest, and are understood to be willing to send Mandzukic in the opposite direction.
The swap may appeal to Mourinho, who has often spoken out about his desire to land a top class centre-forward.
The Croatia international has spearheaded Bayern’s rise to become, arguably, European football’s top club force, but is set to be ousted from his starting role by Robert Lewandowski – who has agreed a Bosman move to the Allianz Arena from bitter rivals Dortmund.
A deal for Atletico Madrid’s Diego Costa to join Chelsea is said to be all but sealed already, but Mourinho could be keen to pair the Spain international with Mandzukic, which could see Luiz head to Munich.