Rangers will face Nordic opposition in their opening Champions League qualifier while Celtic could play fellow former European Cup winners if they progress.
Rangers will take on Malmo or HJK Helsinki while Celtic face a tough task against PSV Eindhoven or Galatasaray if they reach the third qualifying round. The losers of the PSV-Galatasaray tie will take on St Johnstone in the Europa League.
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.
Malmo knocked Ally McCoist's Rangers out of the Champions League qualifiers in 2011 less than a year before the Ibrox club went into liquidation.
The Swedes last reached the Champions League group stages six years ago, after beating Celtic in the play-offs. They also defeated Hibernian in the Europa League in 2013, knocking seven past Pat Fenlon's side at Easter Road.
Helsinki have only played group stage football twice and their only experience of the Champions League proper came in the last century.
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.
PSV, the 1988 European Cup winners, have made the Champions League group stages three times in the past seven years. They reached the last 32 of the Europa League last term.
Galatasaray lost 2-1 to Rangers at Ibrox in a one-legged Europa League play-off last season, but were twice in the Champions League group stages in the previous three campaigns.
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 be away from home against PSV or Galatasaray in the first leg on August 5.
In the Europa Conference League, Hibernian will take on Maltese side Gzira United or Rijeka of Croatia in the third qualifying round if they get past Santa Coloma. The Croatians have twice played Aberdeen in recent seasons, with each side tasting success.
Aberdeen will meet Austria Vienna or Icelandic side Breidablik if they beat BK Hacken. The Austrians have made group stages four times in the past decade, including once in the Champions League. They are favourites to get past Breidablik, who lost home and away to Craig Brown's Motherwell in 2010.
In the champions path, Linfield will take on Shakhtyor Soligorsk of Belarus or Fola Esch of Luxembourg if they get past Borac Banja Luka.
Shamrock Rovers will play Albanian champions Teuta or Inter Club d'Escaldes of Andorra while Connah's Quay Nomads have the prospect of facing Valur or Bodo/Glimt of Norway if they beat Prishtina.
Larne will face Portuguese side Pacos de Ferreira if they spring a surprise against Aarhus, The New Saints will take on Viktoria Plzen or Dynamo Brest if they beat Kauno Zalgiris, and Dundalk will take on Vitesse if they can get past Levadia Tallinn.