Manchester United have been drawn against Istanbul Basaksehir or Copenhagen in the last eight of the Europa League, while Wolves have a potential tie against Sevilla or Roma.
Rangers will play Inter Milan or Getafe if they reach the quarter-finals.
United and Wolves will meet in the semi-finals if both progress.
The three British sides have the second legs of their last-16 ties to play with United 5-0 up on LASK, while Wolves are level at 1-1 with Olympiakos.
Rangers trail Bayer Leverkusen 3-1 after the first leg.
The return legs will take place on 5 or 6 August. United and Wolves are at home, but Rangers travel to Germany.
Draw in full:
5-6 August
Remaining last-16 ties: Copenhagen v Istanbul Basaksehir (0-1), Wolves v Olympiakos (1-1), Bayer Leverkusen v Rangers (3-1), Shakhtar Donetsk v Wolfsburg (2-1), Basel v Eintracht Frankfurt (0-3), Manchester United v LASK (5-0), Inter Milan v Getafe (first leg abandoned), Sevilla v Roma (first leg abandoned).
Quarter-finals, 10-11 August
1. Wolfsburg/Shakhtar Donetsk v Eintracht Frankfurt/Basel
2. LASK/Manchester United v Istanbul Basaksehir/Copenhagen
3. Inter Milan/Getafe v Rangers/Bayer Leverkusen
4. Olympiakos/Wolves v Sevilla/Roma
Semi-finals, 16-17 August
Winner of quarter-final 4 v winner of quarter-final 2
Winner of quarter-final 3 v winner of quarter-final 1
Final, 21 August
