The Reds have been heavily aligned with the 22-year-old in recent months after being impressed with his showings while on loan at Empoli for 2015/16.
However, talk of a move for Zielinski had cooled off, with some speculation suggesting that Mahmoud Dahoud of Borussia Monchengladbach had emerged as a priority target.
However, reports now claim that the Poland international is closing in on a move to Merseyside, with Liverpool and Udinese having come close to sealing an agreement after ‘a few days of reflection’.
Yet, they may have to move quickly, with the likes of Roma and Napoli mentioned as rival suitors.
Should a deal go through, Zielinski will become Jurgen Klopp’s third summer signing after goalkeeper Loris Karius and centre-back Joel Matip, while January addition Marko Grujic is in line to feature for the club in pre-season after spending the end of the campaign just gone back at Red Star Belgrade on loan.