Klopp experimented with sign his fellow German as manager of Borussia Dortmund ahead of the 23-year-old's move from Borussia Monchengladbach to Barca in 2014.
But since moving to your Nou Camp, Ter Stegen has struggled to find out himself as club's first-choice stopper.
Despite being Luis Enrique's No 1 inside Champions League, he remains behind Claudio Bravo within the pecking order for La Liga matches.
And he could be keen to maneuver on with Klopp reported to be ready to put his faith in him.
Current first choice Simon Mignolet originates in for constant criticism since being signed by Brendan Rodgers from Sunderland in 2013.
If Ter Stegen is usually to be the man who will come in to dislodge him frrm his position on Merseyside, then this club should pay a tremendous transfer fee.
While the £56.7million release clause in the contract is actually a stumbling block, Spanish publication Sport claim Liverpool want to do an agreement nonetheless.
Manchester United were also related to a move from the summer as David de Gea was widely likely to be on his another option.
Ter Stegen was viewed as the ideal replacement prior to Spaniard's go on to Real Madrid collapsed.
And they may now miss the opportunity to their rivals regardless of whether De Gea does leave Old Trafford inside the future.
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