The Reds had been linked with a move for the Cologne full back.
Jurgen Klopp has already secured four new signings this summer, with Marko Grujic, Joel Matip, Loris Karius and Sadio Mane all making the move to Anfield.
He is unlikely to end his spending there though and several more arrivals are likely at the club in due course.
One area Klopp may look to improve is the left-back position, with Alberto Moreno once again struggling last season.
Last month Liverpool were linked with Germany defender Hector as a replacement for the Spaniard, with the Daily Mail reporting they had scouted him while he was on international duty.
However, the Mirror then followed that up by reporting their interest had cooled in the Cologne defender in recent weeks and according to Bild, that is because the German side have put a £25 million asking price on their man.
That is a price the Reds are allegedly unwilling to pay and as a result it is believed that Barcelona are now leading the race for Hector's signature.