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Rangers will face Salzburg or FC Twente in the Champions League play-off if they overcome Dynamo Kyiv.
And Hearts will take on Kryvbas Kryvyi Rih or Viktoria Plzen in the Europa League play-off.
Ukraine's Dynamo and Philippe Clement's Rangers meet for the first leg of their third qualifying tie on Tuesday evening in Poland, where Dynamo are temporarily playing because of the Ukraine war. Rangers' home leg will be the following Tuesday at Hampden, with Ibrox currently unavailable due to renovation works.
Austrian Bundesliga runners-up Salzburg host Dutch outfit Twente, who were third in last season's Eredivisie, in Tuesday's first leg, with their return match also next Tuesday.
Rangers, who would be the home team for the first leg on 21 or 22 August, recently sold Sam Lammers to Twente. The second leg would take place the following midweek.
The draw for the revamped Champions League proper takes place on 29 August, with the first of eight rounds of fixtures in mid-September.
Steven Naismith's Hearts, third in last season's Premiership, will be away from home first on 22 August against Ukraine's Kryvbas Kryvyi Rih, who are playing their home ties in Slovakia, or Czech side Viktoria Plzen. The return leg at Tynecaslte will be on 29 August.
Both of the potential opponents finished third in their domestic league last term and Plzen were runners-up in the Czech Cup.
Win and Hearts are through to the league phase, lose and they will enter the Conference League group stage.
Kilmarnock and St Mirren feature in Monday afternoon's Conference League play-off draw.
Killie or Tromso will be in the first group of ties drawn in the Conference League play-off round, with St Mirren or Brann in group two. Frances' Lens are possible opponents for Killie while St Mirren could face Italians Fiorentina.
Kilmarnock and St Mirren both play the home legs of their third qualifying round ties on Thursday, with the return legs the following Thursday in Norway. Killie lost 2-1 to Belgium's Cercle on aggregate to drop into the Conference League while St Mirren beat Iceland's Valur 4-1 over two legs to reach the last round before the group stage.
The play-off ties would be played over the final two Thursdays in August.
The draws for the league phase of the Europa League, of which there will be eight rounds of fixtures, and the Conference League group phase, which has six match nights, will be on 30 August.
The Europa league phase starts on the final midweek of September with the Conference group stage commencing in early October.