The Spanish giants have been strongly linked with the £40million-rated defender this summer.
Barcelona failed with a bid to sign the 26-year-old a year ago, but he is top of the club’s wish-list this summer.
The Mirror reports that Barcelona are confident that a huge offer may tempt Chelsea to sell.
Luiz signed a new long-term contract at Stamford Bridge last summer.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.