Cliftonville will face FC Bate of Belarus or Albanians KS Skenderbeu next if they win their Champions League second qualifier against Debrecen.
Linfield face a trip to Kazakhstan to meet FC Astana if they beat AIK Stockholm in their Europa League tie.
Derry City will meet Waragem of Belgium or Polish club Zawisza Bydgoszcz if they progress from their second leg.
Crusaders, 4-0 down against Swedes Brommapojkarna, are set to miss out on a glamour tie against Torino.
Crues manage Stephen Baxter says his team's tie against Brommapojkarna is over following Thursday's first leg so there will be no trip to Italy for the Irish Premiership side.
FC Astana are 3-0 up from their first leg against Hapoel Tel Aviv while Linfield will be aiming to hold on to their 1-0 advantage against AIK Stockholm.
Even in the unlikely event of Hapoel Tel Aviv over-turning their first-leg deficit against Astana, Linfield will be spared a trip to Israel because that country's clubs have been barred from hosting Uefa matches because of the current conflict in the country.
Israeli clubs must propose alternative home venues to Uefa until further notice.
Derry will face a huge task in over-turning their 1-0 first-leg home defeat by Belarusian side Shakhtyar Soligorsk.
Cliftonville held the Hungarians to a goalless draw in Tuesday's first leg and play the return game next Tuesday.
FC Bate and KS Skenderbeu also didn't produce a goal in their first leg on Tuesday.
Linfield were beaten 3-1 on aggregate by Bate in a Champions League qualifier in 2011.
The Blues drew 1-1 in the first leg at Windsor Park before losing the away contest 2-0 a week later.
The Belarusian club progressed to the group stages of the Champions League in three successive seasons from 2010-11 although they were knocked out in the qualifiers by Shakhter Karagandy of Kazakhstan last year.
KS Skenderbeu had been Albanian champions for the past four seasons but have never progressed to the Champions League group stage.