They delivered on a raucous Anfield night, with a 1-0 win being enough to dump the Serie A side out of the competition and progress themselves.
Liverpool entered the last 16 draw along side Ajax, Atletico Madrid, Barcelona, Bayern Munich, Borussia Dortmund, Juventus, Man City, Man United, Porto, Real Madrid, Roma, Schalke, Lyon, Tottenham and PSG.
As they finished second in their group, they had the possibility of facing Dortmund, Barcelona, Porto, Real Madrid, Bayern Munich or Juventus.
Monday's draw saw them confirmed to face Niko Kovač, who they last met in the UEFA Super Cup in 2001, winning 3-2.
Bayern are currently third in the Bundesliga table, nine points behind rivals Borussia Dortmund.
The first leg between the two sides will be played at Anfield on February 12/13 or February 19/20, with the second leg away from home on either March 5/6 or 12/13.
Liverpool are home in the first leg due to finishing second in their group, although playing away from home in the second leg against Roma and Man City did not hinder them on their run to final last season.
Klopp will be hoping his side can better their final appearance from last season, with heartbreak against Real Madrid in Kyiv still on the minds of many supporters.
Virgil van Dijk will be suspended from the first leg after picking up a booking against Napoli, which is sure to be a big blow for the boss.
Round of 16 draw in full
‣ Liverpool v Bayern Munich
‣ Schalke v Man City
‣ Atletico Madrid v Juventus
‣ Man Utd v PSG
‣ Tottenham v Borussia Dortmund
‣ Lyon v Barcelona
‣ Roma v Porto
‣ Ajax v Real Madrid