Klavan joined the Reds in a deal worth £4.2 million in July, with the Estonian leaving Augsburg after four seasons.
Though something of a surprise target for Liverpool supporters, Klavan had proved himself one of the most consistent defenders in the Bundesliga over that period.
This is so much so that Klopp had tracked his progress while manager with Borussia Dortmund, revealing to reporters on Thursday that he had long planned to sign him for Liverpool.
“I didn’t need to be convinced. With Ragnar it’s quite simple,” he said.
“The first time with Augsburg, I saw him, he was always strong.
“I was surprised Augsburg found a player like him we didn’t know before—I didn’t like this that much!
“We didn’t need a centre-half at Dortmund, but I was always surprised he stayed another year, then another year.
“When I came here and became aware of our situation and what I wanted to change, he was very early a real idea because of his skills.”
Klavan has so far made three appearances for Liverpool, scoring his first goal in Tuesday night’s 3-0 victory away to Derby County in the League Cup third round.
Proving to be an accomplished, ready-made solution at centre-back, Klavan looks to be one of the bargain signings of the Reds’ summer.
As Klopp went on to detail, the 49-year-old felt Klavan’s availability was a “great opportunity” for his side.
“He’s a really good defender with the fantastic [bonus] of being a wonderful football player,” Klopp continued.
“A little issue is he’s not 21 anymore, but he still has four or five great years to go.
“It was a great opportunity, and when I spoke to him I didn’t have to convince him much. I like to work with players who really want to come [here].
“In the beginning a few people were surprised with the name because not a lot of Bundesliga is watched in England.
“But [there are no] questions about his quality anymore.”
Showing the humility to accept these decisions in the first months of his Liverpool career, Klavan is unlikely to complain, and this is clearly a quality Klopp values.