The controversial centre-back's future at Real Madrid is currently in doubt, with there being hints that he could leave the club he joined from Sevilla 15 years ago.
The 34-year-old's contract with the Spanish champions is set to end in the coming summer, and negotiations over a possible new contract have stalled.
As a result of this, several reports are indicating that PSG are monitoring his contract situation very closely, with the idea of offering a very lucrative deal.
The reports add that PSG are willing to offer a deal that is worth as much as a staggering £18 million per season, which will last three years.
Real Madrid are currently looking at making him sign a two-year extension at the club.
Los Blancos manager Zinedine Zidane has stressed the importance of Ramos in his team, saying "We want him here forever, it is what he is doing, showing that he always wants to. I have no doubt that he will stay and that it will continue to make history."