That's according to the Mirror's Matt Lewis, who notes Liverpool boss Jurgen Klopp "is keen to wrap an £11 million move for the central midfielder and had been initially looking at securing his services this January."
However, with the youngster already on loan at Empoli and pursuing a place on Poland's squad for Euro 2016, the Reds will need to wait until the summer—something they're content to do, according to Lewis.
The 21-year-old is one of Serie A's rising stars and has two goals and five assists to his name in 19 league appearances so far this season.
Zielinski is comfortable on the ball and possesses great dribbling skills and the ability to create opportunities for his team-mates, with Squawka reporting the central midfielder has completed 44 take-ons from 63 attempts—an impressive 70 per cent success rate—and created 41 chances.
Football commentator Adam Summerton has repeatedly been impressed with the youngster:
Adam Summerton @adamsummerton
Fantastic character, and a fair bit of quality too in that @EmpoliCalcio side. Impressed again by Piotr Zieliński #EmpoliMilan2016-1-23 21:47:45
With the likes of James Milner, Jordan Henderson, Lucas Leiva, Emre Can and a resurgent Joe Allen among Klopp's central midfield options, central midfield isn't the most pressing area of the field Liverpool need to strengthen.
Nevertheless, Zielinski would make a strong recruit and if he should fulfil his potential at Anfield, he could go on to be a star for the Reds in the future.
Another alternative is Borussia Monchengladbach's Granit Xhaka. According to German outlet Sport Bild (h/t Rory Benson-Le of the Liverpool Echo), Klopp met with his agent in December and is hoping to recruit the Swiss star. However, as sports journalist Stefan Bienkowski notes, Gladbach are firm in their stance:
Stefan Bienkowski @SBienkowski
Gladbach's General Manager has now said Granit Xhaka wont be moving this month for the second time in 2 weeks.2016-1-28 10:38:06
Stefan Bienkowski @SBienkowski
@uersfeld yeah I get why he was asked again. It's just interesting how often they'll have to refute any rumours.2016-1-28 10:45:33
Indeed, per Bild (h/t Alex Richards of the Mirror), general manager Max Eberl said: "I would like to say clearly once again at this point: Granit Xhaka wants to stay in Monchengladbach and we do not want to sell him. He is a super player for us and will contest the second half of the season here."
The 23-year-old is Gladbach's key man in the middle thanks to his metronomic distribution, reminiscent of former Liverpool star Xabi Alonso. Indeed, the youngster was up there with Alonso in terms of passes completed in the Bundesliga last season, per WhoScored.com:
Granit Xhaka: Only Xabi Alonso (2473) completed more passes in the Bundesliga this season than Xhaka (2018) http://t.co/utpU9gDLpj2015-6-1 16:30:35
Bundesliga football expert Clark Whitney believes Xhaka would fit in well at Anfield:
Clark Whitney @Mr_Bundesliga
SportBild: Liverpool have 1st meeting with Xhaka, who'd be a brilliant signing for any of EPL's top sides but esp good fit in Klopp's system2016-1-27 07:07:20
It's clear the Reds will struggle to land him this winter, though, but expect them to pursue him in the summer.
In other news, according to Sky Sports (h/t Rhys Turrell of the Daily Star), Reims have made a loan offer for Liverpool stopper Adam Bogdan in a bid to bring him to France for the remainder of the season.
The Hungarian has failed to make an impact at Anfield since arriving for free in the summer, and an improvement in his playing situation looks unlikely with Simon Mignolet ahead of him.
However, Turrell notes that Klopp is "not keen on the deal," which could indicate Bogdan will be the first-choice replacement for Mignolet should he be injured or suspended despite Danny Ward's return from Aberdeen.