Klopp is a big fan of the Poland international, who has come close to moving to Liverpool in the past.
Calciomercato.com says Liverpool scouts have been watching Zielinski this season and a bid is being prepared for the end of this season.
Zielinski has battled for a regular start this term, but Napoli chiefs still rate the winger at €35-40m.
The midfielder admits he turned down Liverpool ahead of originally joining the Azzurri.
He said: “Everyone said: 'great offer, Klopp wants you, it's a fairytale in terms of finances'. All fine, but I wasn't convinced.
“I was driving my car and I said to my girlfriend: 'No, red light, I'm not leaving'. I felt great in Empoli, I didn't want to leave the lads when we were battling for the European places.