Celtic will face either Romanian side Cluj or Maccabi Tel-Aviv of Israel should they progress to the Champions League third qualifying round.
The Scottish side still have a second qualifying-round tie against Estonian champions Nomme Kalju to navigate as they look to keep alive hopes of making the lucrative group stages.
Neil Lennon’s men saw off Sarajevo in their opening European tie of the new campaign. Should Celtic progress again, the third-round matches will be played on August 6/7 and 13.
Elsewhere in Monday’s draw, Ireland’s Dundalk are set to play either Montenegro club Sutjeska or APOEL of Cyprus in the third qualifying round if they can get past Azerbaijan side Qarabag.
The New Saints of Wales are taking on Copenhagen in the second qualifying round, and the Oswestry side will then meet either HJK Helsinki or Red Star Belgrade.
Sides defeated in this round will transfer to the Europa League champions path play-offs.
The Europa League third-qualifying round draw also took place on Monday, with the main section set to follow after the champions path.
Should Northern Ireland side Linfield get past HB Torshavn, they will play either Sutjeska or APOEL.
The New Saints will face Iceland side Valur Reykjavik or Ludogorets of Bulgaria, if they lose to Copenhagen.
Celtic went into Group Two of the draw, which could potentially see them play either Shkendija of North Macedonia or Luxembourg club Dudelange.
Champions League defeat would send Dundalk into a third-round Europa League qualifying tie against either Slovan Bratislava of Slovakia or Kosovo side Feronikeli.
In the main path Europa League qualifying draw, Premier League side Wolves, who play Northern Ireland’s Crusaders in the second round, were paired against either Pyunik of Armenia or Czech side Jablonec should they progress.
Scottish side Rangers were not among the seeded teams in Group 3, and were drawn against Danish club Midtjylland should they get past Luxembourg side Progres Niederkorn.
Aberdeen were paired against HNK Rijeka of Croatia or Georgian club Chikhura Sachkhere.
Welsh club Connah’s Quay Nomads – set to play Serbian team Partizan – were drawn against the winners of the clash between Turkish side Malatyaspor and Slovenians Olimpika Ljubliana.
Ireland’s Shamrock Rovers were paired against Austria Vienna should they progress against Cypriot club Apollon Limassol.
The third-qualifying round ties will be played on August 8 and 15, with the winners going on to the Europa League play-off round.