Last season's Europa League runners-up Rangers will have to beat either Monaco or PSV Eindhoven to clinch a place in the Champions League group stage, as long as they first make it through the third qualifying round.
The Scottish giants play Union Saint-Gilloise of Brussels, last season's surprise runners-up in the Belgian top flight, in the first leg of their third qualifying round tie on Tuesday.
Should the Glasgow club come through that tie, they face a daunting two-legged showdown against Monaco or PSV later this month.
Monaco, who host PSV in the first leg of the third qualifying round later on Tuesday, finished third in Ligue 1 last season, just missing second place and an automatic berth in the Champions League group stage on the final night of the French campaign.
PSV have appointed former striker Ruud van Nistelrooy as their new coach and beat Ajax 5-3 in the Dutch Super Cup last weekend.
Rangers lost to Eintracht Frankfurt in last season's Europa League final but have not featured in the Champions League group stage since 2010/11.
All bar one of the six ties drawn at Uefa headquarters in Nyon, Switzerland on Tuesday depend on the outcomes of third qualifying round match-ups this week and next.
The sole exception is the tie between Danish champions FC Copenhagen and Trabzonspor, who last season won a first Turkish title since 1984.
Teams who won their national leagues are paired in the qualifying rounds and kept apart from clubs who entered the competition despite a lower league placing.
The six winners from the play-off round will join 26 automatic qualifiers in the draw in Istanbul for the group stage on August 25.
The final of this season's Champions League will be played in the Turkish city on June 10, next year.
Uefa Champions League play-off round draw:
Qarabag (AZE) or Ferencvaros (HUN) v Sheriff Tiraspol (MDA) or Viktoria Plzen (CZE)
Bodo/Glimt (NOR) or Zalgiris Vilnius (LTU) v Ludogorets Razgrad (BUL) or Dinamo Zagreb (CRO)
Maccabi Haifa (ISR) or Apollon Limassol (CYP) v Red Star Belgrade (SRB) or Pyunik (ARM)
FC Copenhagen (DEN) v Trabzonspor (TUR)
Dynamo Kyiv (UKR) or Sturm Graz (AUT) v Benfica (POR) or Midtjylland (DEN)
Union Saint-Gilloise (BEL) or Rangers (SCO) v Monaco (FRA) or PSV Eindhoven (NED)
- First legs to be played on August 16/17, second legs on August 23/24