With Alex out until January and John Terry struggling with injury, Carlo Ancelotti is desperate to find defensive cover.
Benfica star Luiz is valued at £25 milion, and the 23-year-old is growing in reputation with every game.
Luiz has won three international caps for Brazil.
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The Mirror are also talking up a potential Bayern Munich swoop for Arsenal's Nicklas Bendtner.
The 22-year-old is reportedly frustrated at his lack of first-team action at the Emirates and Bayern advisor Franz Beckenbauer claimed the club are monitoring his situation.
Bayern could be joined by Juventus is a bidding war for the Danish international, although Arsenal are not keen on selling their young striker.
Source: DSG
