Off contract in June, Rudiger is resisting Chelsea attempts to secure him to a new deal as he considers his options.
BILD says PSG chief Leonardo is making a move for Rudiger and has met with his minders in recent days.
PSG president Nasser Al-Khelaifi is expected to put in a call to the Germany international once he is clear to negotiate with foreign teams from January 1.
Real Madrid are also maintaining contact with Rudiger's agents.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!