Mundo Deportivo claims that one of Philippe Coutinho's agents recently offered the Catalans the chance to sign the Brazil centre-back alongside the Liverpool ace this month but manager Ernesto Valverde has alternative plans to bolster his back-line.
Luiz, 30, has been tipped to leave Stamford Bridge since Antonio Conte left him out of the squad for the 1-0 victory over Manchester United on 5 November.
The former Paris Saint-Germain star returned to action days later in a Champions League clash with Qarabag but he has not played a game for Chelsea since then due to an ill-timed knee injury.
Andreas Christensen has since established himself as Conte's first choice to lead his three-man defence and it has been said that Luiz is likely to leave Chelsea in order to cement his place in the Brazil squad for the upcoming World Cup this summer.
Real Madrid, Arsenal and Newcastle are said to be monitoring the situation while Barcelona have also been linked with his services in recent times, with the Catalans expecting to lose Mascherano to Hebei China Fortune this month.
Mundo Deportivo says that one of Coutinho's agent, Giuliano Bertolucci, personally offered Barcelona the possibility of signing Luiz to replace the Argentina international as the agent of the Liverpool star also represents the Chelsea defender.
Prestigious agent and his partner Kia Joorobchiam are currently in regular contact with Barcelona due to their ongoing negotiations over the Liverpool playmaker.
However, Mundo Deportivo says that Barcelona told the agents of the Liverpool star that they are not interested in Luiz due to different reasons.
Valverde does want a new defender to replace Mascherano but the Barcelona boss is looking for someone to be a back-up for Gerard Pique and Samuel Umtiti and cannot see Luiz accepting a role as a substitute. Furthermore, the Spanish publication points out that the Chelsea defender would be cup tied for the Champions League while his lucrative salary will also be a problem for Barcelona.
The Catalans plan to pay in excess of €100m sign Coutinho from Liverpool and cannot afford to make another big investment.
Mundo Deportivo says Barcelona have two cheaper alternatives to bolster the back-line in the form of Colombia international Yerry Mina and another unidentified experienced centre-back which would accept being a mere back-up for Pique and Umtiti.
One way or another Luiz's future at Chelsea remains up in the air after Conte himself recently suggested that he won't stand in the way of the defender or Michy Batshuayi if the two decide they want to leave Stamford Bridge to secure regular time elsewhere.
"I was a player, I will understand if someone is worried about the World Cup," Conte recent said. "I understand it's very important to keep players very happy to stay here to work with us and I think this must be our priority. To keep the players happy to stay with us, to continue to work with us. At the same time, I was a player and I will understand if someone is thinking in this way (that they need to play more),"
"I prefer to have players very happy to stay here than to have players that are unhappy because when you are unhappy you transfer this to the other players, to me, to my staff and I don't like this. If we can avoid this, I'd like to avoid this situation."