United, winners of the European trophy in 2017, beat Barcelona in the playoff stage before cruising past Real Betis in the round-of-16. They face another LaLiga side in Sevilla, who hold the record number of Europa League titles.
Erik ten Hag will be looking to add the Europa League as his second trophy in his debut season as United boss after winning the Carabao Cup in February. United also remain in this season's FA Cup and play Fulham in the quarterfinals on Sunday.
United will be looking to avoid a repeat of the 2020 semifinals between the two sides when Sevilla secured a 2-1 victory and went on to win the competition.
United could face former boss Mourinho in the final with Ten Hag's side and Roma on opposite sides of the draw. He spent two years at Old Trafford from 2016-18 and guided the club to their last European title.
The winners of the tie between United and Sevilla will visit the victors of Juventus and Sporting's clash in the semifinals.
The Europa League quarterfinals will be played across two legs on April 13 and April 20. The two-legged semifinals will be staged on May 11 and May 18 before the final at the Puskas Arena in Budapest, Hungary on May 30.
Europa League quarterfinal draw:
Manchester United (England) vs. Sevilla (Spain)
Juventus (Italy) vs. Sporting CP (Portugal)
Bayer Leverkusen (Germany) vs. Union SG (Belgium)
Feyenoord (Netherlands) vs. AS Roma (Italy)
Europa League semifinal draw:
Juventus/Sporting CP vs. Manchester United/Sevilla
Feyenoord/AS Roma vs. Bayer Leverkusen/Union SG