The Brazilian international is wanted by the Camp Nou outfit as they look to bolster their defence.
Mundo Deportivo claim that Luiz wants the move and will press Chelsea to let him leave for Barcelona.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.