READ: Champions League quarter-final draw
Villarreal were pitted with Sparta Prague, and Braga will take on Shakhtar Donetsk in the other last-eight fixtures.
The match-ups were decided by a draw in Nyon, Switzerland on Friday, with the two-legged ties scheduled for 7 April and 14 March.
Quarter-final ties:
Braga vs Shakhtar Donetsk
Villarreal vs Sparta Prague
Athletic Bilbao vs Sevilla
Dortmund vs Liverpool