If Sligo can complete the job against Rosenborg after their shock 2-1 win in Norway yesterday they will face Turkey's Kardemir Karabukspor in the Europa League third qualifying round.
Derry City’s reward should they fight back from a 1-0 first-leg home defeat to win their tie against Belarus’ Shakhtyor Soligorsk will be a clash with either Zulte Waregem of Belgium or Zawisza Bydgoszcz of Poland.
And if Dundalk can emerge triumphant from the second leg of their tie against Hajduk Split in Croatia, which they will head into 2-0 down, their opponents in the next round will be Lithuanians FK Atlantas or Shakhter Karagandy of Kazakhstan.
As for Danske Bank Premiership sides, it will be Italy’s Torino for Crusaders if they pull off an unlikely-looking aggregate victory over IF Brommapojkarna, to whom they trail 4-0 from the first leg in Sweden.
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 are set to be played on July 31, with the second legs on August 7.
Hull will begin their debut European campaign with a tie against either AS Trencin of Slovakia or Serbia’s Vojvodina.
The Slovakian side have a 4-0 lead over Vojvodina from the first leg of their second-round tie.
If Motherwell come through their second-round 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.
The draw for the UEFA Europa League Third Qualifying round is as follows:
Karabukspor v Rosenborg/Sligo Rovers
Chornomorets v RNK Split/Hapoel Beer
Sheva Lucerne/St Johnstone v FC Zestafoni/FC Spartak Trnava
Mainz v RoPS/Asteras Tripolis
Litex Lovech/Diosgyor VTK v Sillamae Kalev/Krasnodar
Mlada Boleslav/Siroki Brijeg v Lyon
AS Trencin/Vojvodina v Hull
Buducnost Podgorica/Omonia Nicosia v Metalurg/Zeljeznicar Sarajevo
Torino v Brommapojkarna/Crusaders
PSV v Botev Plovdiv/SKN St Polten
Motherwell FC/Stjarnan v Nomme Kalju/Lech Poznan
Laci/FC Zarya Lugansk v Molde FK/HiT Gorica
FK Sarajevo/Haugesund v Atromitos
Real Sociedad v Aberdeen/FC Groningen
Astana/Hapoel Tel-Aviv FC v Linfield/AIK Zulte
Waregem/Zawisza Bydgoszcz v Derry City FC/Shakhtyor Cukaricki
Belgrade/SV Grodig v CSKA Sofia/FC Zimbru
FC Astra Giurgiu v MFK Kosice/Liberec
Ruch Chorzow/FC Vaduz v Kairat Almaty/Esbjerg
Dinamo Moscow v Hapoel Kiryat Shmona
Young Boys v Ermis Aradippou
IF Elfsborg/Inter Baku v Neman/FH Hafnarfjordur
Petrolul Ploiesti /Flamurtari Vlore v Plzen
Vikingur/Tromso v Rijeka/Ferencvaros
Dinamo Minsk/MyPa v CFR Cluj-Napoca/FK Jagodina
Neftchi/Koper v Bursaspor/Chikhura
Sachkhere Gyori/IFK Goteborg v Rio Ave
Club Brugge v Brondby
FK Atlantas/Shakhtyor Karagandy v Dundalk/Hajduk Split
Ties to be played 31 July and 7 August