Buvac remains a Liverpool employee and his position will not be affected by his absence, the club says.
It means Liverpool manager Juergen Klopp will be without his assistant of 17 years for the second leg of the Champions League semifinals against Roma on Wednesday. Liverpool leads 5-2 from the first leg at Anfield last week.
Klopp and Buvac played together at Mainz in the early 1990s. They were reunited when Klopp made him his assistant after becoming Mainz coach in 2001 and were also together at Borussia Dortmund from 2008-15.
According to numerous reports from journalists on Merseyside, Buvac is known as 'the brain' due to his imperative input when it comes to tactics, starting line-ups and training sessions.
The timing is questionable, with Liverpool set to play Roma in the second leg of the UEFA Champions League semi-final on Thursday morning, and then should they progress the final against either Bayern Munich or Real Madrid on May 27.
"One theory is Buvac has grown frustrated by a perceived dilution of his responsibilities, while Kornmayer, recruited from Bayern Munich two years ago, has been recommended to receive a new contract. Many have noticed of late that Buvac has seemed more distant," the Daily Mail's Liverpool correspondent, Dominic King, reported.
Respected German journalist, Raphael Honigstein, said that the relationship between Buvac and Klopp "has been volatile at times."
"They’re both impulsive characters but always came back together eventually," Honigstein tweeted.