Arsenal have been drawn against Napoli, while Chelsea will face Slavia Prague in the Europa League quarter-finals.
Villarreal take on fellow Spanish side Valencia with Portuguese team Benfica playing Germany’s Eintracht Frankfurt.
The first and second legs will be played on 11 April and 18 April, with the semi-final draw keeping Arsenal and Chelsea apart should they get that far.
Arsenal boss Unai Emery is chasing a fourth Europa League title as manager after three successive wins at Sevilla.
The Gunners reached the last-eight after overturning a 3-1 deficit to beat French side Rennes 3-0 in the second leg of their last-16 tie.
Should Chelsea win the Europa League, as they did in 2013, it would offer them an alternative route to next season’s Champions League.