The draw for the next stage of the competition was made on Friday morning.
Toulouse, who finished third in France's Ligue 1 last season, will host Rafael Benitez's Reds in the first leg.
Arsenal will go to the Czech Republic capital for the first leg against Sparta.
Celtic will meet Spartak Moscow, with the first leg in the Russian capital.
If, next Tuesday, Rangers get past Montenegro's FK Zeta in the second qualifying round - the Gers lead 2-0 from the first leg at Ibrox - they will meet either Serbia's Crvena Zvezda, otherwise known as Red Star Belgrade, or Estonia's Levadia Tallinn.
Belgrade won 1-0 at home to Levadia in Wednesday's first leg.
The first leg matches will be played on Tuesday 14/ Wednesday 15 August, with the second legs on 28/29 August.
Draw for the UEFA Champions League third qualifying round:
FH Hafnarfjordur/BATE v Zaglebie Lubin/Steaua Bucuresti
Levski Sofia/Tampere United v FC Astana/Rosenborg
Spartak Moscow v Celtic
Werder Bremen v Domzale/Dinamo Zagreb
FK Ventspils/SV Red Bull Salzburg v Shakhtar Donetsk/Pyunik
Ajax v MSK Zilina/Slavia Prague
Valencia v Debrecen/IF Elfsborg
Genk/FK Sarajevo v Dynamo Kiev
Fenerbahce v Anderlecht
Rangers/Zeta v Crvena Zvezda/Levadia Tallinn
Toulouse v Liverpool
Benfica v FC Copenhagen/Beitar Jerusalem
Lazio v Dinamo Bucuresti
Sparta Prague v Arsenal
FC Zurich v Besiktas/FC Sheriff
Sevilla v AEK Athens