The Bosnian, who has worked with Klopp for 17 years, is spending some time away from the first team from now until the end of the season for personal reasons.
Speculation began circulating on Sunday the Bosnian had quit but the club have dismissed that by stressing Buvac remains a Liverpool employee and his position is not affected by this absence.
It is understood the club considers the matter to be private and therefore will respect that privacy by not making any further comment.
Klopp is unlikely to offer any more on the matter at his pre-match press conference when the team arrive in Rome today.
It is not the best preparation for tomorrow’s Champions League semi-final second leg against Roma in the Stadio Olimpico, which is followed by a crucial Premier League encounter at Chelsea on Sunday.
The Reds hold a 5-2 lead from the first leg against the Italians, while in the league they sit six points clear of fifth-placed Chelsea, who have a game in hand.
“Again, two massive games — what a season,” Klopp said.
“You play the whole season (and) we created a basis and now we have to finish it. There are a few things to do.
“You work for that the whole season, it’s really exciting.
“Let’s play the next game, try to make the best of it, then we’ll see.”
It will have to be achieved without assistant coach Buvac — whom Klopp has described as ‘The Brain’ of his backroom team — who was on the touchline for Saturday’s goalless draw at home to Stoke but will not be travelling to Italy.
There are still some concerns about the safety of the 5,000 fans heading to Rome after 53-year-old Irishman Sean Cox was attacked before the first leg at Anfield.
Arrangements are still being made but a plan has been put in place and guidance issued to supporters to try to minimise the chance of more trouble.
Travelling fans are being asked to register their details with the club, providing information such as how and when they are arriving and leaving.
Advice issued includes respecting monuments of national importance with a particular emphasis placed on not hanging banners and/or scarves on fountains and statues, avoiding areas in the north of the city, particularly those in the vicinity of Ponte Milvio Bridge, on match day, and using the shuttle bus service to and from the game.
Italian police have advised that drinking in the streets will be prohibited from today until Thursday as will carrying bottles or glass containers.