Celtic will face either Legia Warsaw or St Patrick's in the Champions League third qualifying round if they come through their tie against KR Reykjavik, while Hull kick off their Europa League campaign against AS Trencin or Vojvodina.
The Scottish title winners secured a 1-0 first-leg victory over their Icelandic opponents away from home on Tuesday in what was new Hoops boss Ronny Deila's first game in charge.
The second leg is next Tuesday, 24 hours before League of Ireland Premier Division champions St Patrick's host Polish side Legia in the return leg of their tie, the opening encounter of which finished in a 1-1 draw.
2014 FA Cup finalists Hull -- who will play in European competition for the first time -- look most likely to meet Slovakian side AS Trencin, who have a 4-0 lead over Serbians Vojvodina from the first leg of their second-round Europa tie.
In other Champions League games, Cliftonville of the Danske Bank Premiership have been drawn to face either Belarus' BATE Borisov or Albanian outfit KS Skenderbeu if they get past Hungarians Debrecen, who they drew 0-0 with at home this week.
Meanwhile, the reward for Welsh Premier League champions The New Saints -- if they can bounce back from their 1-0 first-leg loss to Slovan Bratislava in Slovakia and win the tie -- will be a clash with either FC Sheriff of Moldova or FK Sutjeska of Montenegro.
Other notable ties in the third qualifying round see Feyenoord take on Besiktas, Grasshoppers play Lille and Standard Liege face Panathinaikos.
The first legs are set to be played on July 29 and 30 with the second legs on Aug. 5 and 6.
If Motherwell come through their second-round Europa League encounter with Icelanders Stjarnan -- the first leg of which finished 2-2 in Scotland -- they will take on Nomme Kalju of Estonia or Lech Poznan of Poland.
Aberdeen will have a tough task ahead if they progress from their tie against FC Groningen, with Spain's Real Sociedad lying in wait for the winners. The Dons fought out a 0-0 first-leg draw with the Dutch outfit at Pittodrie on Thursday.
Meanwhile, Scotland's other participants St Johnstone will play Zestafoni of Georgia or Spartak Trnava of Slovakia should they get past Luzern following a 1-1 first-leg draw in Switzerland.
And progression by Linfield -- 1-0 winners in their first leg at home against another Swedish side, AIK -- will set up a meeting with either FC Astana of Kazakhstan or Israeli side Hapoel Tel-Aviv.
The third-round first legs take place on July 31, with the second legs on Aug. 7.