Luiz has been in and out of the Chelsea side this season under Jose Mourinho and the Blues would contemplate selling the Brazilian for £35million.
Current PSG defender Alex is out of contract in the summer although the French league leaders are hoping to fend off interest from Napoli and Barcelona for his services by giving him a new deal.
Luiz is seen as the long term partner to compatriot Thiago Silva at the back for the big spending Paris side.
Chelsea boss Jose Mourinho yesterday admitted that he may need to sell some players in the summer to balance the books; however he was referring to the likes of Romelu Lukaku and Thibaut Courtois who are currently out on loan.
Barcelona made an approach for Luiz back in the summer which was swiftly dismissed by the Blues, but if John Terry signs a new deal with the West London club Luiz could be set for another season playing a bit-part role.