Luiz is undergoing a medical ahead of a proposed transfer which would make the Brazilian football's most expensive defender.
The 27-year-old appears surplus to requirements at Chelsea, who recently gave skipper John Terry a one-year extension to his contract and used Gary Cahill at centre-back for most of the season.
Branislav Ivanovic is also capable of playing as a centre-back, and Mourinho - who has used Luiz predominantly as a defensive midfielder - is also known to be a fan of rising youngster Tomas Kalas.
Luiz joined Chelsea from Benfica in 2011, in a £23.5m deal during the January transfer window, and he still has two years left on his contract at Stamford Bridge.
But Mourinho now looks set to more than double Chelsea's money, and that cash could go towards a huge bid for Atletico Madrid striker Diego Costa.
Qatar Sports Investments have ploughed millions into PSG, allowing them to sign the likes of Zlatan Ibrahimovic and Edinson Cavani. They were knocked out of the Champions League by Chelsea in the quarter-finals this season.
The French giants were fined £48.5m by UEFA this month for breaching the Financial Fair Play rules.
But coach Laurent Blanc says that will not stop him improving his squad, and admitted to Le Parisien newspaper he is a big fan of another Chelsea star, Eden Hazard, without revealing whether he would make a bid.
"Hazard is the kind of player who can be decisive," Blanc is quoted as saying.
"You can talk about all kinds of things; tactics, strength of the team, individual class, but a player who is capable of beating three or four players is something else. You never know what to expect from him."
But Blanc confirmed winger Jeremy Menez is definitely leaving and former Chelsea defender Alex could also be on his way out as he tries to make room in his squad for new signings.