Celtic or Linfield could face Irish champions Dundalk in the Champions League's third qualifying round.
Dundalk face a difficult second leg in Norway after drawing 1-1 at home to Rosenborg on Wednesday.
But they have the incentive of facing British Isles opposition, with Linfield hosting Celtic in their first leg in Belfast on Friday, if they win.
Welsh champions The New Saints will face Hibernians of Malta or Salzburg of Austria if they beat Croats Rijeka.
Red Bull will almost certainly be hosting the first leg of the third qualifying round after establishing a 3-0 lead in Malta.
But TNS will themselves have to come from 2-0 behind when they host Rijeka if they are to set up a likely meeting with the Austrians.
The winner of Celtic v Linfield will be at home in their first leg of the next round following Friday's draw in Nyon.
Rosenborg will be favourites to provide the opposition and are in fine form, leading the Norway's top flight by five points from Brann Bergen after 16 games of the 2017 season.
The Troillongan, who include former Arsenal striker Nicklas Bendtner in their squad, are seeking their third straight domestic title.
Dundalk qualified for the group stages of last season's Europa League but are unlikely to retain their domestic title for a third season.
The side, managed by former Dunfermline Athletic manager Stephen Kenny and captained by former Falkirk midfielder Stephen O'Donnell, are 12 points behind Cork City 20 games into in the League of Ireland season.
Dundalk's Oriel Park home is unlikely to be used if they progress to the next round.
However, the Aviva Stadium is unavailable on 2 August, one of the dates earmarked for the second leg, because of a friendly between Manchester United and Sampdoria.
French side Nice, with former Liverpool striker Mario Balotelli in their ranks, take on four-time winners Ajax of the Netherlands in the round's stand-out tie.
Champions League third qualifying round draw
Slavia Praha (Czech Republic) v BATE Borisov (Belarus) or Alashkert (Armenia)
Spartaks Jurmala (Latvia) or Astana (Kazakhstan) v Mariehamn (Finland) or Legia Warszawa (Poland)
Zrinjski (Bosnia-Herzegovina) or Maribor (Slovenia) v Hafnarfjördur (Iceland) or Víkingur (Faroe Islands)
Zilina (Slovakia) or Copenhagen (Denmark) v Malmo (Sweden) or Vardar (Macedonia)
Linfield (N Ireland) or Celtic (Scotland) v Dundalk (Ireland) or Rosenborg (Norway)
Hapoel Beer-Sheva (Israel) or Honved (Hungary) v Zalgiris Vilnius (Lithuania) or Ludogorets (Bulgaria)
Viitorul (Romania) v APOEL (Cyprus) or Dudelange (Luxembourg)
Hibernians (Malta) or Salzburg (Austria) v Rijeka (Croatia) or The New Saints (Wales)
Qarabag (Azerbaijan) or Samtredia (Georgia) v Sheriff Tiraspol (Moldova) or Kukesi (Albania)
Partizan (Serbia) or Buducnost Podgorica (MNE) v Olympiacos (Greece)
Steau Bucaresti (Romania) v Viktoria Plzen (Czech Republic)
Nice (France) v Ajax (Netherlands)
Dynamo Kyiv (Ukraine) v Young Boys (Switzerland)
AEK Athens (Greece) v CSKA Moskva (Russia)
Club Brugge (Belgium) v Istanbul Basaksehir (Turkey)