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He impressed enough to attract attention from Liverpool, who handed him a three-year contract in October 2015 after sacking previous coach Brendan Rodgers.
The 53-year-old has since transformed the Reds from also-rans back into English football's most formidable side, delivering the club'sfirst top-flight title in three decades and a sixth European Cup.
The Merseyside outfit are gunning for more silverware in the 2020-21 campaign, and Krueger says Klopp is still trying to enhance his skills on the touchline as he continues to cement an everlasting legacy at Anfield.
"I once had a long chat with Jurgen Klopp, that was on the sidelines of a game in Liverpool." the ex-Southampton chief, who is now the head coach of NHL team the Buffalo Sabres, told Goal and SPOX.
"He knows very well that, with Southampton and Virgil van Dijk, we are also indirectly part of the development in Liverpool.
"(laughs) When we talk about Jurgen Klopp, we also have to talk about the owners of the Reds. I also got to know them during my time in England, they had the necessary patience and allowed Jurgen to go his own way and build up his culture.
"Today everyone only sees the great successes of the last few years, but these successes did not come overnight. A few years ago, Liverpool only played the Europa League - people tend to forget that.
"I am most impressed by his honest culture. Players have a say with him, he doesn't work with pressure or fear. Jurgen leads with love and honesty. In addition, there is a very clear plan behind the emotionality and passion, a very clear structure.
"And Jurgen also works in such a way that he wants to keep learning personally. For me, he is one of the greatest coaches at the moment - in all sports."
Klopp will start preparing his side for a crucial encounteragainst Leicester after the international break, with the Reds currently trailing the Foxes by a point at the top of the Premier League table.