According to the Liverpool Echo, the Reds continue to search for a new attacking option and has identified the 23-year-old as a potential signing.
The Merseyside giants have a strong relationship with the Bundesliga outfit, having previously acquired players including Sadio Mane, Naby Keita, Takumi Minamino and also the most recent addition Ibrahima Konate.
The 25-year-old has made 180 appearances for PSG in all competitions, including 40 outings during the last campaign.
Kimpembe could face a battle for his spot next term, though, following the arrival of Sergio Ramos, and according to L’Equipe, the Frenchman could consider his future away from the French capital.
United boss Ole Gunnar Solskjaer has been tipped to bring in a new centre-back to play alongside Harry Maguire for the long-term, and Varane has supposedly been identified as the club’s top target.