Linfield will play Malmo of Sweden or Lithuania’s FK Zalgiris Vilnius if they make it through to the Champions League third qualifying round.
The Blues must first get past Norwegian champions Bodø/Glimt in the second round, the first leg of which is at Windsor Park on Tuesday night.
Crusaders will play Polish club Pogon Szczecin or Brondby if they beat Basel in the Europa Conference League.
The Blues and Crues both won their opening European ties last week.
If Linfield beat the Norwegian champions in the second qualifying round, they will be at home in the first leg of the third qualifying round, which would take place on 2 August.
Blues could face Qarabag again
Defeat against Bodø/Glimt would see the Irish Premiership champions drop into the third qualifying stage of the Europa League, with Monday’s draw dictating that they would play either Qarabag or FC Zurich in that.
David Healy’s men had a memorable battle with the Azerbaijani outfit in 2019 when, despite a superb solo goal from striker Shayne Lavery, Qarabag pipped Linfield for a place in the Europa League group stages.
In the Champions League, Shamrock Rovers will play Dinamo Zagreb or FC Shkupi in the third qualifying round if they get through.
The League of Ireland Premier Division champions are up against PFC Ludogorets of Bulgaria in the second round.
Linfield, who have won the Irish Premiership title for four consecutive seasons, defeated Welsh champions The New Saints in the opening round of Champions League qualifiers.
They were on the verge of going out before a stunning strike from captain Jamie Mulgrew four minutes into injury time forced extra time, with substitute Ethan Devine hitting the winner.
The Blues lost to Zalgiris in the Champions League first qualifying round last season.
Crusaders secured their place in the Europa Conference League second qualifying round after an injury-time goal from Billy Joe Burns secured them a 4-3 aggregate success over Bruno’s Magpies of Gibraltar.
The Crues will be away to Basel in the second round first leg tie on Thursday before the home game with the Swiss outfit on 28 July.
If they do progress to the third round, they will again face an away opener against Pogon Szczecin or Brondby on 4 August before the home leg seven days later.
League of Ireland outfit Sligo Rovers will take on either Sparta Prague or Viking of Norway should they get past Motherwell in round two while St Patrick’s Athletic’s reward for overcoming Mura of Slovenia would be a third qualifying round tie against CSKA Sofia or FK Makedonija.
