The Reds have already snapped up Schalke defender Joel Matip on a pre-contract agreement, whilst Mainz goalkeeper Loris Karius is on the verge of a move to Anfield according to The Guardian, and Polish newspaper Przeglad Sportowy believe Udinese midfielder Piotr Zielinski is also joining Klopp's side.
All of those players will add something to the Liverpool squad, but fans may be keen to see a big name arrive this summer - and Klopp could be plotting a move for one of his former players.
The Sun report that Liverpool are pushing ahead with a deal for Bayern Munich star Mario Gotze, and want a £20m deal completed this coming week.
It was Klopp who gave Gotze his big break at Borussia Dortmund, and the playmaker racked up 31 goals in 116 appearances at Signal Iduna Park before his controversial 2013 move to rivals Bayern Munich.
With 30 goals in his first two seasons as well as a World Cup winner's medal having scored the winning goal in the 2014 final against Argentina, Gotze's move to Bavaria appeared to be paying dividends at club and international level.
However, Gotze has fallen out of favour under outgoing manager Pep Guardiola, starting just 14 games in all competitions this term, notching only six goals and four assists.
Now, Klopp wants to rescue Gotze and rekindle their relationship from their Dortmund days, and it's believed that with Liverpool looking to do their transfer business early, a £20m deal will be targeted this week ahead of the European Championships.
Liverpool already have a host of playmakers such as Philippe Coutinho, Roberto Firmino and Adam Lallana, but adding a player of Gotze's undoubted quality would be a huge coup - and it's a reunion with Klopp which could tempt the playmaker into joining the Reds this week.
Would you like to see Liverpool sign Gotze?