Stoke know their fate already, with a clash against Hajduk Split already decided, while Fulham may have to face RNK Split if they can get past Domzale of Slovenia.
The Cottagers won the first leg of their second round clash with Crusaders 3-1 on Thursday while RNK Split were winning their away leg 2-1 to make them favourites to progress.
Hearts will take on either Hungarian side Paksi or Tromso of Norway.
And Dundee United could face Metalurg Skopje of Macedonia or Levski Sofia of Bulgaria if they get through their second round clash.
The Tannadice side have an uphill task, though, having gone down 1-0 to Slask Wroclaw in Poland on Thursday.
The Europa League third Qualifying Round draw is as follows:
Third Qualifying Round
Atletico Madrid v Stromsgodset Young Boys v TPS/Westerlo Shakhter/FK Ventspils v Crvena Zvezda Alania Vladikavkaz v Kecskemeti TE/Aktobe Floriana/AEK v Mlada Boleslav Zeljeznicar Sarajevo/FC Sheriff v Khazar Lenkoran/Maccabi Tel Aviv AZ v Flamurtari/Jablonec Olimpija Ljubljana/Bohemians v Rudar Pljevlja/FK Austria Vienna Bursaspor v Gomel Ferencvaros/Aalesund v FK Suduva/IF Elfsborg Minsk/Gaziantepspor v Legia Warsaw Hapoel Tel-Aviv v FC Vaduz/Vojvodina Olimpi Rustavi/Irtysh v Rennes Levski Sofia v SK Tirana/FC Spartak Trnava The New Saints FC/FC Midtjylland v Guimaraes Dinamo Bucuresti v FC Iskra-Stal/Varazdin Karpaty Lviv v Shakhtyor Karaganda/St Patricks Vllaznia Shkoder/FC Thun v Palermo KR Reykjavik/MSK Zilina v Llanelli/Dinamo Tbilisi Omonia Nicosia v FC Tauras/ADO Den Haag SK Liepajas Metalurgs/SV Red Bull Salzburg v FK Senica Club Brugge v EB Streymur/FK Qarabag FC 03 Differdange/Levadia Tallinn v Rad Belgrade/Olympiacos Volou Mainz v KUPS Kuopio/Gaz Metan UE Sant Julia/Bnei Yehuda v Helsingborgs IF Stoke v Hajduk Split FC Gagra/Anorthosis Famagusta v Juvenes/Dogana/Rabotnicki Kometal Orebro SK/FK Sarajevo v Sparta Prague Glentoran/Vorskla Poltava v Sligo Paks/Tromso v Hearts Metalurg/Lokomotiv Sofia v Slask Wroclaw/Dundee Utd FH Hafnarfjordur/Nacional v BK Hacken/FC Honka SV Ried v Brondby PAOK Salonika v Mika Ashtarak/Valerenga Domzale/RNK Split v Crusaders/Fulham
Third round ties to be played 28 July and 4 August.