0602 GMT April 22, 2021
United will host the first leg against Milan, which will see its former striker Zlatan Ibrahimovic return to Old Trafford, skysports.com reported.
Arsenal will travel to Greece in the first leg of its tie with Olympiakos, which knocked it out of the Europa League in the round of 32 last season.
The Greek champion plays its home matches at the Karaiskakis Stadium, the venue for Arsenal's dramatic victory over Benfica in the last 32 of the competition on Thursday.
The Gunners' north London rival Tottenham will face Dinamo Zagreb, which progressed to the last 32 after beating Russian side Krasnodar.
Spurs won the UEFA Cup — the previous incarnation of the Europa League — in 1972 and 1984, while their manager Jose Mourinho lifted the trophy with Porto in 2003 and Manchester United in 2017.
All four British teams left in the competition were kept apart after Rangers were drawn to play Slavia Prague, which shocked Leicester in the previous round.
Elsewhere in the draw, former Arsenal boss Unai Emery — the most successful manager in the history of the Europa League — will see his current side Villarreal take on Dynamo Kiev.
Roma will play 2009 UEFA Cup winner Shakhtar Donetsk, while the 1992 champion Ajax will face Swiss side Young Boys.
Granada will continue its impressive campaign against Norwegian side Molde. The Spanish club is enjoying its first season in European competition and stunned Italian giant Napoli in the previous round.
The first legs of the last-16 ties will take place on March 11, with the return legs a week later.
The quarterfinal and semifinal draws will then be held on March 19 in Nyon, Switzerland.
Europa League last-16 draw:
Ajax vs. Young Boys
Dynamo Kiev vs. Villarreal
Roma vs. Shakhtar Donetsk
Olympiakos vs. Arsenal
Dinamo Zagreb vs. Tottenham
Manchester United vs. AC Milan
Slavia Prague vs. Rangers
Granada vs. Molde
Ibrahimovic's reunion with Manchester United makes for a mouthwatering tie.
The 39-year-old striker established himself as a fan favorite during his short spell at Old Trafford, scoring in the Community Shield and EFL Cup triumphs in 2016-17.
Ibrahimovic played a key role in that season's victorious Europa League run, but a serious knee injury in the quarterfinal triumph against Anderlecht ruled him out of the remainder of the campaign.
The veteran only made seven more United appearances after that and looked set to wind down his career when he moved to LA Galaxy in March 2018, but the striker has flourished since returning to Milan and passed a landmark 500 career club goals earlier in February.