Camp Nou officials contacted Chelsea about the Brazilian shortly before Christmas and Goal understands that the Brazilian is keen to discuss a move away from Stamford Bridge.
Chelsea is willing to listen to formal offers for the 26-year-old, but Jose Mourinho considers the former Benfica man a valuable asset and would only sanction a move for a significant fee.
Barcelona, which is looking to bolster its defensive options with skipper Carles Puyol coming to the end of his career and only Javier Mascherano, Gerard Pique and Marc Bartra as recognized center backs, approached Chelsea over the summer but Luiz claims he rejected the chance to join the Catalan outfit.
"There was an official offer [from Barcelona], but I decided to stay at Chelsea," the defender told Brazilian newspaper Gazeta Esportiva in September.
Mourinho moved to play down talk of any potential transfer last month, stating: "He’s our player and we are happy he’s back in a moment when we need him and John Terry in defense.”
However, sources close to the club have indicated that Chelsea would be willing to let Luiz, who has impressed in recent weeks, leave the club if Barcelona make an offer that is too good to turn down.
Chelsea has been tracking Saint-Etienne defender Kurt Zouma in recent weeks, with the club set to go head-to-head with Manchester City and a number of other sides in the coming months to secure the highly rated 19-year-old.