The Reds are set to lose Sadio Mane to the African Cup of Nations in January and it has been suggested that Jurgen Klopp may move to bring in cover.
According to Corriere dello Sport, Amsterdam-born winger Narsingh is a potential target for the Anfield boss.
The 26-year-old has been a key player for PSV since his arrival in 2012, making 110 Eredivisie appearances for the club, scoring 21 goals.
The Netherlands international could now be offered a chance in England by Liverpool, should they decide to fill the void left by Mane.