Ole Gunnar Solskjaer’s United, who beat AC Milan in the last 16, are due to play away in the first leg on April 8 but it remains to be seen where that match will take place.
The Old Trafford club faced Spanish opponents in Real Sociedad in the last 32 but the first leg of that tie was moved to Turin in Italy because of restrictions on travel from the UK to Spain as a result of the pandemic.
Granada are in Europe for the first time after finishing seventh in LaLiga last season.
The team from southern Spain notably beat PSV Eindhoven away in the group stage and eliminated Napoli in the last 32 before defeating Solskjaer’s old club Molde of Norway in the round of 16.
Granada coach Diego Martinez has won the Europa League before, during his time as an assistant coach at Sevilla.
Meanwhile, Ajax will face Roma with the winners of that quarterfinal playing either United or Granada in the last four. United beat Ajax in the 2017 Europa League final.
Arsenal are set to host Slavia in the first leg of their quarterfinal and will be wary of the runaway Czech league leaders who have eliminated Leicester City and Scottish champions Rangers in the last two rounds.
However if the Gunners get through they could face their former coach Unai Emery in the semifinals.
Emery’s Villarreal will take on Dinamo Zagreb, last-16 conquerors of Tottenham Hotspur, in the other quarterfinal.
Emery took Arsenal to the final of the Europa League in 2019, when they lost to Chelsea in Baku.
The final of this season’s competition is set to be played in the Polish city of Gdansk on May 26.
Granada vs. Man Utd
Arsenal vs. Slavia Prague
Ajax vs. Roma
Dinamo Zagreb vs. Villarreal