Klopp and Krawietz, who have been overseeing training all week, were joined by Buvac, with the Bosnian receiving his work permit on Wednesday morning.
With many of his squad still away on international duty, Klopp is preparing for Saturday’s clash with Tottenham Hotspur with a handful of his key players missing.
Alberto Moreno, Emre Can, Mamadou Sakho, Lucas Leiva, Philippe Coutinho, Daniel Sturridge and James Milner were among those to take part in Wednesday’s session, and are all likely to start at White Hart Lane.
Joao Carlos Teixeira and Dejan Lovren are part of a group looking to impress their new manager, after struggling to impose themselves on Brendan Rodgers’ first-team selection this season.
Lucas described his first training sessions under Klopp as “very positive.”
“He seems to be very passionate – he likes to put in everything that he has and he asks the players for the same,” the Brazilian continued.
“Be very intense, be aggressive with yourself, is what he has been saying.”
Buvac and Krawietz both left Borussia Dortmund when Klopp resigned, and will provide tactical input and opposition analysis respectively.
Klopp will be hoping for a bright start to his life as Liverpool manager with a win over Spurs, and the work he and his staff oversee in these training sessions will be vital.