The Reds got the better of FC Gomel in the last qualifying round and will have to get past the Edinburgh club in the two-legged play-off tie that is scheduled for later this month.
Newcastle United have been drawn against Atromitos of Greece, while Scottish side Motherwell will confront Spanish outfit Levante.
Atromitos could prove to be a tough challenge for Alan Pardew’s Newcastle, with the Athens-based side finishing fourth in the Greek Super League.
They were 23 points adrift of champions Olympiacos, with whom Newcastle drew 1-1 in a friendly in Portugal last month.
Italian giants Inter Milan have been paired against Vaslui, while Steve McClaren’s Twente will entertain Bursaspor in a couple of the other interesting ties.
Full Europa League play-off draw:
Anzhi Makhachkala v AZ
2 APOEL FC v Neftci
Atromitos v Newcastle
Tromso v FK Partizan
Vaslui v Inter Milan
Hearts v Liverpool
Athletic Bilbao v HJK Helsinki
Maritimo v FC Dila Gori/Anorthosis Famagusta
Molde v Heerenveen
Debrecen v Club Brugge
Sheriff Tiraspol v Marseille
Trabzonspor v Videoton
FC Midtjylland v Young Boys
Slask Wroclaw v Hannover 96
Dinamo Bucurest v FC Metalist Kharkiv
AC Horsens v Sporting
Hapoel Tel-Aviv v F91 Dudelange
Feyenoord v Sparta Prague
Motherwell v Levante
Crvena Zvezda v Bordeaux
Lokeren v Plzen
Lazio v Mura
AIK v CSKA Moscow
Legia Warsaw v Rosenborg
Bursaspor v FC Twente
Steaua Bucuresti v Ekranas
Liberec v Dnipro
VfB Stuttgart v Dinamo Moscow
PAOK v Rapid Vienna
Luzern v Genk
Zeta v PSV
Ties to be played 23rd and 30th August