Celtic have been drawn against Kairat Almaty of Kazakhstan or Slovakian side Slovan Bratislava in their Champions League play-off tie, while Rangers could face RB Salzburg.
Brendan Rodgers' side reached the knockout round play-off stage of the competition last season from the 36-team league phase, where they lost 3-2 on aggregate to German giants Bayern Munich.
Celtic began the defence of their Premiership title with a 1-0 win over St Mirren at Parkhead on Sunday.
Rangers will take on Austrian side Salzburg or Club Brugge of Belgium in the play-off round if they get through their third qualifier against Viktoria Plzen.
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The Light Blues take on the Czech side in the first leg at Ibrox on Tuesday night.
Russell Martin's side, who reached the third qualifier with a 3-1 aggregate win over Greek side Panathinaikos, drew 1-1 with Motherwell in their league opener at Fir Park on Saturday.
Both Old Firm clubs are at home for the first leg, which will be played on Aug. 19 or 20. The return fixture will take place on Aug. 26 or 27.