Rafael Benitez's men will face Welsh side Total Network Solutions over two legs, with the first at home.
The winner of the tie will play Faroe Island team HB or Lithuanian side Kaunas in the second qualifying round.
First qualifying round draw
Liverpool v TNS
FC Haka v Pyunik
HB Torshavn v FBK Kaunas
FC Levadia Tallinn v Dinamo Tbilisi
NK Gorica v KF Tirana
FC Kairat Almaty v FC Artmedia Bratislava
PFC Neftchi v FH Hafnarfjordur
Rabotnicki v Skonto FC
Glentoran v Shelbourne
Dinamo Minsk v Anorthosis Famagusta
Sliema Wanderers v FC Sheriff
F91 Dudelange v NK Zrinjski
(Ties to be played over two legs 12/13 July and 19/20 July)
Second qualifying round draw
FC Kairat Almaty or FC Artmedia Bratislava v Celtic
HB Torshavn or FBK Kaunas v Liverpool or TNS
Glentoran or Shelbourne v Steaua Bucharest
Levadia Tallinn or Dinamo Tbilisi v Brondby
Partizan Belgrade v Sliema Wanderers or Sheriff Tiraspol
Debrecen v Hajduk Split
NK Gorica or SK Tirana v CSKA Sofia
Anderlecht v FH Neftchi or Hafanarjordur
Valerenga v FC Haka or FC Pyunik
Rabotnicki or Skonto Riga v Lokomotiv Moscow
F91 Dudelange or Zrinjski Mostar v Rapid Vienna
Dynamo Kiev v FC Thun
Malmo v Maccabi Haifa
Dinamo Minsk or Anorthosis Famagusta v Trabzonspor
(Ties to be played over two legs 26/27 July and 2/3 August)
