The Reds have never lost a two-legged continental tie under the boss, winning all the previous 10 en route to reaching the 2015-16 Europa League final and back-to-back Champions League finals in 2017-18 and 2018-19.
Liverpool beat Tottenham Hotspur 2-0 at Atletico's Estadio Metropolitano last June to claim the club's sixth European Cup and are now seeking to become the first English club in history to reach three successive Champions League finals.
For more need-to-know pre-match facts and figures, courtesy of club statistician Ged Rea, read on...
In 19 away games in Spain, Liverpool have won seven, drawn five and lost seven.
This is the Reds' fifth successive European campaign in which they have faced Spanish opposition. They have only been eliminated by clubs from Spain twice in the previous 11 two-legged ties.
The last La Liga side to do so was Atletico Madrid in 2009-10, when Los Rojiblancos beat Rafael Benitez's side on away goals in the semi-finals of the Europa League.
Liverpool and Atleti have also met before in the Champions League - drawing 1-1 home and away in the group phase of the 2008-09 edition.
Roberto Firmino has played in 47 of Klopp's 48 European games in charge of the Reds.
The Brazilian has four assists in the Champions League this season - only Hakim Ziyech of Ajax (five) has more.
Firmino has scored more goals away from Anfield (39) than any current Liverpool player - seven more than Mohamed Salah and 10 more than Sadio Mane.
Alex Oxlade-Chamberlain has scored three goals in his last three Champions League games and five in his 11 European appearances for the Reds.
Salah has scored 20 Champions League goals for Liverpool and is the club's joint-third highest scorer in Europe, alongside Ian Rush. Steven Gerrard tops the list with 41, while Michael Owen has 22.
Salah's 20 goals in this competition for Liverpool have come in just 33 appearances.
Liverpool have not lost a knockout phase tie in the Champions League since 2008-09, when Chelsea beat them in the quarter-finals.
In European competition, Atletico are unbeaten in their last 13 games at home, winning 11 with two draws.
In 13 matches against English clubs at home, Los Rojiblancos have won seven and drawn five with one defeat.
Only Real Madrid and Barcelona have beaten Atletico in their last 40 matches at Estadio Metropolitano.