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.
The last-16 ties between Inter Milan and Getafe and Sevilla and Roma will both be played as one-off matches in Germany after the coronavirus outbreak in Italy and Spain in March resulted in both first legs being called off.
The last three rounds, which will also see all ties played as one-off matches, will then be held in Germany at the home grounds of Duisburg, Fortuna Dusseldorf, Schalke and Cologne.
The latter venue will host the final, which has been moved from Gdansk in Poland, on 21 August.
Uefa says that the games will be held without spectators present.
Draw in full
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