Neil Lennon's side were paired with the Swedish champions or Latvians FC Daugava in the draw for the competition's third qualifying round.
Elfsborg hold a 7-1 first-leg lead in their second-round tie with Daugava, while Celtic will defend a 3-0 lead over Cliftonville in Glasgow next week.
If the Scottish champions come through unscathed they will host Elfsborg on July 30/31 before travelling to Scandinavia a week later.
Elsewhere, the draw threw up the prospect of a Welsh-Irish meeting between The New Saints and Sligo Rovers, but both must overturn second-round deficits for that to happen.
Sligo were beaten 1-0 at home by Molde in the first leg of their tie, while Legia Warsaw left north Wales with a 3-1 lead.
Champions League qualifying is split into two competitions, one for league winners and another for teams that finished second, third or fourth last season.
Teams progressing through the third qualifying round will then play a final qualifier, with five teams from each competition entering at the group stage in September.
Full third-round qualifying draw:
Nordsjaelland v Zenit St Petersburg
Salzburg v Fenerbahce
PAOK v Metalist Kharkiv
PSV Eindhoven v Zulte Waregem
Lyon v Grasshoppers
Basel v Gyori/Maccabi Tel Aviv
Sligo Rovers/Molde v The New Saints/Legia Warsaw
Slovan Bratislava/Ludogorets Razgrad v Shirak/FK Partizan
Dinamo Tbilisi/EB/Streymur v FC Steaua Bucharest/Vardar
APOEL v Birkirkara/Maribor
Celtic/Cliftonville v Elfsborg/FC Daugava
BATE Borisov/Shakhter Karagandy v Neftci/Skenderbeu
Austria Vienna v Ekranas/Hafnarfjordur
HJK Helsinki/Nomme Kalju v Viktoria Plzen/Zeljeznicar
Fola Esch/Dinamo Zagreb v Sheriff/Sutjeska
Games to be played 30/31 July, and 6/7 August