The Ligue 1 champions are keen to partner Luiz with fellow Brazil international Thiago Silva at the heart of their defence.
But the Stamford Bridge club would be unlikely to accept such a low offer for a player only signed two years ago.
As a result, it may only be the opening gambit in negotiations between Paris St Germain and Chelsea.
Luiz is a hugely popular figure at Stamford Bridge, but speculation over his future in west London has intensified since Jose Mourinho took over as Chelsea boss earlier this month.
And the Brazilian international put PSG on alert this week when he admitted he's interested in the "project" currently underway in the French capital.
PSG, who won the Ligue 1 title last season, will be looking to fend off a fresh challenge from fellow big-spending French outfit Monaco next season.
And they see Luiz as the type of ball-playing centre-half capable of propelling them permanently into the upper echelons of Europe's elite.
The former-Benfica star swapped Portugal for Chelsea in 2011, but reports also carried by Portuguese newspaper A Bola claim Paris St Germain's interest in the defender is real.
The centre-back is currently with Brazil at the Confederations Cup.