Manchester United will face Spanish side Real Sociedad in the last 16 of the Europa League, while Tottenham will play AZ Alkmaar and Rangers meet Jose Mourinho's Fenerbahce.
Should United advance, they will play Romanian league leaders FCSB or Lyon in the quarter-finals.
Spurs or Dutch side AZ Alkmaar will face Eintracht Frankfurt or Ajax in the last eight, while Rangers will meet Roma or Athletic Bilbao if they get past Turkish club Fenerbahce.
With Manchester United and Tottenham on opposite halves of the draw, they could - in theory - meet in the final in Bilbao on 21 May, knowing the winner would earn Champions League football next season.
With the Premier League all but guaranteed five places in the Champions League next season, an all-Premier League final would probably mean a sixth English club in Europe's premier club competition in 2025-26 - as Spurs and United are unlikely to finish in the top five.
Meanwhile, Chelsea will face FC Copenhagen in the last 16 of the Conference League.
United, Spurs and Rangers are all away in the first leg of their last-16 ties on Thursday, 6 March. The return legs take place on 13 March.
Chelsea will travel to Denmark for the first leg against Copenhagen on 6 March, with the return at Stamford Bridge seven days later.
Europa League last-16 draw in full
Bodo/Glimt v Olympiakos
Fenerbahce v Rangers
Ajax v Eintracht Frankfurt
FCSB v Lyon
AZ Alkmaar v Tottenham
Real Sociedad v Manchester United
Viktoria Plzen v Lazio
Roma v Athletic Bilbao
Europa Conference League last-16 draw in full
Jagiellonia Białystok v Cercle Brugge
Molde vs Legia Warsaw
Celje vs Lugano
Pafos vs Djurgarden
Panathinaikos vs Fiorentina
Borac Banja Luka v Rapid Vienna
Real Betis vs Vitoria Guimaraes
FC Copenhagen v Chelsea