The centre-back spent two years in the French capital from 2014 to 2016 after joining the club in a £50million deal from Chelsea.
Luiz rejoined the Blues, before moving to Arsenal in 2019 for a fee of around £8m.
However, he was released at the end of last season after the Gunners opted against extending his deal and Luiz had been expected to rejoin another of his former clubs, Benfica.
But Le10Sport claim PSG president Nasser Al-Khelaïfi remains a huge admirer of Luiz and wants him to make a return to the club this summer.
Luiz was a favourite of the PSG owners and he still shares a friendly relationship with Al-Khelaifi.
The Ligue 1 giants could comfortably cover Luiz’s wages but a final decision will be left with Mauricio Pochettino, who is yet to be convinced that the veteran has it in him to play regularly in the French capital.
PSG’s rivals, Rennes and Marseille, are both said to be interested in Luiz with Marseille in talks with the defender over a two-year deal.
Luiz has reportedly spoken at length with Marseille boss Jorge Sampaoli to discuss a move to the south coast but Luiz is in no rush to make a decision.