The Reds have been very quiet in the market, signing left-back Kostas Tsimikas from Olympiakos.
According to the Athletic, Klopp wants to add more depth to his squad this summer.
But only if they are the right fit for his squad, and financially viable for the club.
Winger Ismaila Sarr from Watford is another target.
The Reds will likely have to sell fringe players to raise funds and make squad space for new arrivals.