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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.