New Bayern boss Pep Guardiola is said to be an admirer of the Brazilian international and wants to make him his second signing for he summer, following the arrivals of Mario Gotze and Thiago Alcantara.
The Sun claim Bayern made an informal approach over the availability of Luiz during the Confederations Cup final last month.
The German giants lost 4-2 against rivals Borussia Dortmund in the Super Cup over the weekend - their first game under Guardiola.
The Sun report that the former Barcelona boss believes that the game highlighted a weakness at the back, and that he is ready to offer a package that could be worth up to £45 million including bonuses.
It has been suggested that new Chelsea boss Jose Mourinho was open to selling Luiz this summer and it was reported he was offered as part of the Blues bid for Wayne Rooney, something that was quickly denied.
Chelsea paid Benfica around £21 million for Luiz back in 2011.
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