Heart of Midlothian will meet Fenerbahce or Gornik Zabrze if they get past Sturm Graz in Champions League qualifying.
Rangers were seeded in the Europa League third qualifying round and were drawn against Polish side Jagiellonia Bialystok.
If Hearts lose to the Austrians, Benfica or St Gallen of Switzerland await in the Europa League.
Fenerbahce and Gornik Zabrze finished as runners-up last season in Turkey and Poland respectively, with Jagiellonia Bialystok behind the latter on goal difference.
Third-round qualifying ties in the Champions League are scheduled for 4/5 and 11/12 August, with Europa League games on 6 and 13 August. Dates and home and away details are yet to be fully decided.
Hearts, who play their first leg in Graz on Tuesday, last took part in Champions League qualifying in 2006-07, losing out at the third qualifying round stage to AEK Athens.
Last term, Rangers started in Champions League qualifying and finished 32nd in the 36-team Europa League league phase after picking up just one win from eight games.
Motherwell and Hibernian await news of their potential Conference League opponents.
The Fir Park side take on Faroese outfit HB, with LNZ Cherkasy (UKR)/Gent (BEL), Besiktas (TUR)/FC Midtjylland (DEN), HJK Helsinki (FIN)/Coleraine (NIR), Twente (NED)/Ferencvaros (HUN) or RFS (Lat)/Vestri (ISL) waiting for the winners.
Meanwhile, Hibs are up against Kosovan side FK Malisheva with their possible next-round opponents coming from NK Bravo (SVN)/KF Shkendija (MKD), FC Santa Coloma (AND)/SK Rapid (AUT), Rakow (POL)/Valetta (MLT), NK Rijeka (CRO)/Derry City (IRL) or FC Polissya (UKR)/FC Copenhagen (DEN).
