Ligue 1 big-spenders eye Reds target.
The Ligue 1 giants are possibly set to lose Edinson Cavani to Arsenal in the near future, and are scouring the market for replacements upfront, with Benzema emerging as one of their top targets.
The French international forward has recently been linked with a move to Liverpool, who are still looking for new signings upfront to help replace Luis Suarez after his £75m move to Barcelona in the summer.
Benzema has been a key player in his time at Real, and formed part of their Champions League-winning squad last season after striking up a fine understanding with team-mates Cristiano Ronaldo and Gareth Bale.
However, Real could continue to make changes to their squad as they have also let key players such as Mesut Ozil, Angel Di Maria and Xabi Alonso leave the club in recent times, much to the frustration of the Bernabeu fans.
Benzema could be next to go, despite recently signing a new contract running until 2019, and PSG will hope to beat Liverpool to his signature if he does become available in the near future.