Rangers will take on Malmo or HJK Helsinki in their opening Champions League qualifier.
Celtic face a tough task against PSV Eindhoven or Galatasaray if they reach the third qualifying round.
Steven Gerrard’s seeded side were drawn out of the pot second and face a trip to Sweden or Finland for the first leg on August 3-4.
Malmo will host Helsinki – the former club of Gers striker Alfredo Morelos – in the first leg of the second qualifying round on Wednesday.
The Hoops are also due to be away for the first leg, if they can get past Midtjylland. Ange Postecoglou kicks off his Celtic reign against the Danish side at Parkhead on Tuesday.
Celtic will play Jablonec in the Europa League if they cannot get past Midtjylland, with the first leg in the Czech Republic.
St Johnstone will play the losers of the PSV-Galatasaray Champions League clash in the third qualifying round of the Europa League. Saints will be away from home in the first leg on August 5.