England's Hallam Hope in action against Poland's Piotr Zielinski
The Reds have already signed up four players for next season, as goalkeeper Loris Karius, defender Joel Matip and midfielder Marko Grujic will all join up with the Liverpool squad this summer.
However, manager Klopp will still be looking to bring in some more new faces, and reports suggest he could be on the verge of landing a player currently at Euro 2016.
The Guardian report that Liverpool have submitted a £9.5m bid to sign Udinese midfielder Piotr Zielinski, who has been out on loan with their Serie A rivals Empoli for the past two seasons.
Zielinski, 22, hit five goals and four assists for Empoli last season, and he could now follow in the footsteps of Polish international team-mates Lukasz Piszczek, Jakub Blaszczykowski and Robert Lewandowski in working under Klopp, after those three starred for the German at Borussia Dortmund.
It's claimed that Liverpool have offered £9.5m to sign Zielinski, but they're still £2.5m away from Udinese's £12m asking price - and Napoli are hovering around the situation too.
However, it's believed that manager Klopp called Zielinski on Saturday to discuss the move, reassuring the midfielder that he will play an important role for Liverpool both next season and beyond, which Liverpool will hope puts them in pole position for Zielinski's signature.
Would you like to see Liverpool sign Zielinski?