Celtic face a tough task against PSV Eindhoven or Galatasaray if they reach the third qualifying round of the Champions League.
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.
Rangers will take on Malmo or HJK Helsinki in their opening Champions League qualifier. 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 3rd-4th. Malmo will host Helsinki — the former club of Gers striker Alfredo Morelos — in the first leg of the second qualifying round on Wednesday.
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 5th.
Meanwhile, Callum McGregor has spoken of the “great honour” of being named the new Celtic captain by Postecoglou.
The 28-year-old midfielder, who came through the club's academy system, takes over from Scott Brown who departed for Aberdeen in the summer.
McGregor had a loan spell at Notts County earlier in his career before making his Hoops debut in 2014 in a Champions League qualifier against KR Reykjavik in Iceland, when he scored the only goal of the game.
Capped 34 times for Scotland, he has made 326 appearances, scoring 53 goals, and has won 14 trophies — six league titles, four Scottish Cups and four League Cups.
McGregor told the club’s website: “To be the Celtic captain is a great honour for any player, and to be given the captaincy is a very proud moment for me and my family.
“I know I’m following in the footsteps of some great names in the club’s history, and I’ve been able to learn from one of the best in Scott Brown over the past few years.
“I’m delighted that the manager has put his trust in me by giving me the captain’s armband.
“It’s a new era for the club and I’m looking forward to playing my part in that.”
Postecoglou said: “Callum is a player who leads by example, both on and off the park, and he is a key figure in our squad.
“He has been at Celtic since he’s been a boy, he’s come through our academy, had a loan spell away from the club to gain vital experience, and then returned to establish himself in the first-team.
“His qualities as a player are there for all to see, and that has been evident over the past few years.
“He knows what it takes to be a successful Celtic player and he knows what it means to captain this club, and I’m delighted that he will be wearing the armband and leading the squad going forward.”