The Pole has been one of the most impressive performers for the Serie A side in recent years and has a couple of goals from eight league appearances this season.
The report adds that Jurgen Klopp is an admirer of the 24-year-old and tried to sign him in 2016. Zielinski was starring for Udinese then but decided to stay in Italy and moved to Napoli.
The report claims that Juventus are also interested in the Napoli man. The Serie A giants have made it a habit of poaching players from rival clubs such as Gonzalo Higuain and Miralem Pjanic in recent seasons.
Liverpool did sign midfield reinforcements in the summer with Fabinho and Naby Keita joining. However, neither star has become a regular starter for the side as Klopp prefers a trio of Georginio Wijnaldum, Jordan Henderson and James Milner.
Zielinski would be a great acquisition for the club, but we will have to wait and see how this progresses in the coming weeks.