The pair worked with Klopp as his assistants at Borussia Dortmund and were expected to follow him to Merseyside.
Klopp has wasted no time in shaking things up at Anfield, with ex-manager Brendan Rodgers' former allies Gary McAllister and Sean O'Driscoll already relieved of duties.
Buvac, nicknamed "The Brain", is a former team-mate of the new Liverpool boss from their time at Mainz and they worked together at the club as manager and assistant later down the line.
They linked up again when Klopp took the Dortmund job and took his most trusted ally with him.
GETTY
Jurgen Klopp has brought Zeljko Buvac with him to Liverpool
GETTY
Peter Krawietz has also followed Klopp to Merseyside
Meanwhile, video analyst Krawietz has no playing experience but comes highly rated by the Liverpool boss-in-waiting and is set to follow suit.
It is also thought the former Dortmund chief will now consider raiding his old club's playing staff.
Midfielder Ilkay Gundogan has already moved to wish Klopp well on Merseyside, while Marco Reus, Neven Subotic and Henrikh Mkhitaryan have all been linked with switches to join their old manager.
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