The Brazil defender has been top of Barca's transfer shortlist since the beginning of the summer, as the Spanish giants scour Europe for a world-class centre-back.
Luiz has emerged as one of Chelsea's key players since his transfer from Benfica in January 2011, but Nou Camp president Sandro Rossell has reportedly tested the water regarding a move.
If he receives any indication that Chelsea would be willing to negotiate, the report claims he'll return with a final offer.
The Catalans have been frustrated in their pursuit so far, with Chelsea refusing to entertain bids for the Brazilian defender and they even rejected a Barca offer for Luiz last summer.
He signed a new long-term deal at the club at the end of the 2011-12 season, but Barcelona hope new recruit Neymar will help persuade Luiz to join the La Liga side.
Neymar is Barca's sole big-money deal this summer, with the Brazilian striker joining from Santos in a deal reportedly worth €57m.
The report claims they don't plan to go anywhere near that kind of money for Luiz - a bid around the £30m mark is more likely - but they believe such an offer could tempt the Blues.
Bayern Munich have also been mentioned as possible Luiz suitors, but the European champions have recently denied the speculation.