New owner Todd Boehly is continuing to shake things up after sacking Thomas Tuchel and replacing him with Graham Potter as he also wants to hire Campos, 58, as the club's new director of football.
Le Parisien says the Blues have offered the Portuguese executive an estimated £135,000 per week to take charge of the next two transfer windows.
Boehly will also hand the PSG chief a whopping €300m (£261m) transfer kitty to land Potter's top targets come January.
There is no clause in Campos' contract with the French champions that prevents him from accepting Chelsea's bid.
However, the same reports suggest PSG would be entitled to some compensation.
