At Mainz they secured promotion to the Bundesliga for the first time in the club's history in 2004, and at Borussia Dortmund they secured the title and reached a Champions League final, losing to Bayern Munich.
Klopp would often call on Buvac's wisdom in helping to make substitutions to help impact a game in Liverpool's favour, while the Bosnian would also be partially responsible for helping the Reds win their "tactical battles" in some of the club's bigger games.
His importance to Klopp was underlined at the end of the 2015/16 season, as when the manager was given a six-year deal by Liverpool, he insisted on similar contract lengths for both Buvac and fellow coach Peter Krawietz.
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Before their winning streak, the Canucks had a chance at finishing last overall to get an 18.5% chance at the first overall pick. Carolina is searching for a general manager after Ron Francis was reassigned to another front-office position last season.
However, the Anfield club maintain Buvac remains a employee of the club. Buvac was present for the goalless draw with Stoke City 24 hours earlier, but will not fly out to Rome with the rest of the Reds' travelling party on Tuesday.
This comes after the Daily Record reported that Buvac, who moved to Anfield in October 2015, has left the club following a "dispute" with Klopp. In the past, he was the only one who had Klopp's ear. He's the one I've learned the most from.
Liverpool supporters will have received yesterday's news with a feeling of unease given parallels from their recent past, and the fact that Buvac is not the first to leave Klopp's backroom staff this season following Pepjin Linders' decision to become head coach of NEC Nijmegen in January.
Klopp has described Buvas as "the brain" behind his coaching set-up in the past, and his absence is an unwanted distraction as Liverpool look to hold onto their 5-2 first leg lead against Roma.