United, semifinalists last season, reached the last eight after Paul Pogba's goal saw them beat AC Milan 1-0 at San Siro, and will face Granada who are in the quarterfinals for the first time. The La Liga side reached this stage with a stunning win over Napoli before beating Molde in the round of 16.
Arsenal are looking to go one better than 2019 when they were beaten finalists, but will have to overcome a Slavia side who have so far eliminated Leicester City and Scottish champions Rangers.
Villarreal boss Unai Emery, who won this competition in three consecutive years with Sevilla, is bidding to become the first manager to win a European competition on four occasions. They will face Dinamo, who reached the last eight after a stunning comeback victory over Tottenham Hotspur in the round of 16.
Should Villarreal progress to the final, they could meet Arsenal, who Emery had guided to the 2019 final.
Ajax have a tricky quarterfinal tie with Roma where, if they win, could meet United in the semifinal in a repeat of the 2017 final.
The quarterfinal first legs will be played on April 8 with the returns on April 15, while the first semifinals will be on April 29 and second legs to take place on May 6. The final will be played in the Polish city of Gdansk on May 26.
Granada vs. Manchester United
Arsenal vs. Slavia Prague
Ajax vs. Roma
Dinamo Zagreb vs. Villarreal
Granada or Manchester United vs. Ajax or Roma
Dinamo Zagreb or Villarreal vs. Arsenal or Slavia Prague