The report claims the World Cup winner is set to be appointed at the Parc des Princes on Monday, with former-PSG manager Carlo Ancelotti tipped to take over at Real Madrid.
Luiz has been targeted by La Liga rivals Barcelona in recent weeks, with speculation mounting over his future at Stamford Bridge under new boss Jose Mourinho.
The 26-year-old centre-back is prone to mistakes and his high risk, high reward defensive style doesn't fit in with Mourinho's conservative instincts.
The ball-playing Brazilian international is currently at the Confederations Cup, but the report claims PSG will consider an offer in the few days after Blanc's appointment.
Luiz has been identified as a replacement for Brazil bound Alex. The 31-year-old former Chelsea defender wants to return to South America, and PSG are keen to partner Luiz with international teammate Thiago Silva.
Luiz has been in the wars at the Confederations Cup, breaking his nose during Brazil's match against Mexico last week.
The Chelsea man will need surgery, and played against Italy in their final group game on Saturday before he was substituted after 33 minutes - a 4-2 victory for the host nation.
They will play Uruguay in the semi-final, with Spain facing Italy in the second semi-final.