Olympiakos will be favourites to be Rangers' next opponents should the Scots progress
Rangers will face either Olympiakos of Greece or Ludogorets of Bulgaria in the Champions League play-offs if they defeat Malmo in their qualifier.
Lose that and Rangers will play Kazakhstan's Kairat or Armenia's Alashkert in a Europa League play-off.
Celtic will face AZ Alkmaar should they win their opening tie in that, while St Johnstone may take on Randers.
Aberdeen could face Limassol or Qarabag in the Conference League with Hibernian taking on Bohemians or PAOK.
A play-off against the Irish or Greeks for Hibs is dependent on Jack Ross' side overcoming Rijeka of Croatia, while the Dons must defeat Breidablik of Iceland if they are to face either the side from Cyprus or from Azerbaijan.
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To earn a tie against Danish side Randers, St Johnstone must overcome Galatasaray of Turkey, while Celtic have to defeat Jablonec of Czech Republic to secure a showdown with Netherlands' AZ.
Lose out and Saints will face either Vojvodina of Serbia or LASK of Austria in a Conference League play-off, while Celtic's next opponents will be Tobol of Kazakhstan or Zilina of Slovakia should they suffer defeat.
Teams to progress after next week's second leg of the Champions League third qualifying round will face play-off round ties on 17/18 and 24/25 August.
First legs of the Europa League and Conference League play-offs are on 19 August with the return seven days later.
Who are the Scottish sides' potential opponents?
Olympiakos won the Greek Super League for a 46th time, while the Bulgarians from Razgrad lifted their domestic First League for the 10th time in succession.
Ludogrets are currently ranked 58th in Europe, six places below Rangers, with Olympiakos 21 ahead of the Ibrox side.
The Greeks are looking to reach the Champions League group stage for the fourth time in five years and lost to Arsenal in the last 16 of the Europa League last season.
Ludogorets finished bottom of their Europa League group last season but have Champions League group experience in 2014-15 and 2016-17.
Kairat of Almaty, who won Kazakhstan's Premier League for the third time, knocked Aberdeen out of the qualifying rounds in 2015-16 but have yet to reach a group stage.
That season, Alashkert, who last season won Armenia's Premier League for a fourth time, defeated St Johnstone in Europa League qualifying before losing to Kairat.
Alkmaar enter at the play-off round after finishing third in the Eredivisie last season.
They were unbeaten in their first 32 European home matches until losing to Everton in 2007 and did not lose in four European home games last term. The Dutch side finished third in their Europa League group, taking four points off Napoli, after dropping out of the Champions League qualifiers.
Tobol of Kostanay were runners-up in the Kazakhstan Premier League and defeated Astana to win last season's domestic Super Cup.
Zilina were fourth in Slovakia's Fortuna Liga last season and lost to Slovan Bratislava in the Slovak Cup final.
Randers, who have yet to progress to a European group stage, were sixth in the Danish Superliga but qualified for the Europa League with a 4-0 thumping of SonderjyskE in their domestic cup final.
Vojvodina, who finished fifth in the Serbian SuperLiga, have also never reached a group stage but famously lost to Celtic in the quarter-finals as the Glasgow side went on to lift the European Cup in 1967.
LASK were fourth in the Austrian Bundesliga last season, lost 3-0 to league champions Red Bull Salzburg in their domestic cup final and finished third ahead of Ludogorets in a Europa League group won by Tottenham Hotspur.
Limassol were runners up to Omonia in last season's Cypriot First Division and defeated Vllaznia Shkoder of Albania in the last round to give themselves a chance of reaching a group stage for the first time since the Europa League in 2012-13.
Qarabag, who were also runners-up in their domestic league, lost 1-0 on aggregate to Celtic in a Champions League play-off in 2015 before becoming the first Azerbaijani club to reach the group stage two years later.
Bohemians, who were runners-up in the League of Ireland Premier Division, have already gone further in European competition than ever before but have previously lost to Aberdeen (twice), Rangers (twice) and Dundee United in European competition.
PAOK, who have the joint most appearances in the Europa League group stage with eight, were runners-up in the Greek Super League but turned the tables on Olympiakos by beating the champions in the domestic cup final.
Champions League play-off draw
Malmo (Sweden) or Rangers v Olympiakos (Greece) or Ludogorets 1945 (Bulgaira)
Europa League play-off draw
Jablonec (Czech Republic) or Celtic v AZ Alkmaar (Netherlands)
Malmo (Sweden) or Rangers v Kairat Almaty (Kazakhstan) or Alashkert (Armenia)
Randers (Denmark) v Galatasaray (Turkey) or St Johnstone
Europa Conference League play-off draw
Bohemian (Ireland) or PAOK (Greece) v Hibernian or Rijeka (Croatia)
Jablonec or Celtic v Tobol Kostanay (Kazakhstan) or Zilina (Slovakia)
Limassol (Cyprus) or Qarabag (Azerbaijan) v Breidablik (Iceland) or Aberdeen
Vojvodina (Serbia) or LASK (Austria) v Galatasaray or St Johnstone
Home side for first leg listed first