Manchester United will face Spanish side Granada in the Europa League quarter-finals, with a box office semi-final against one of Ajax or Roma lying in wait for Ole Gunnar Solskjaer's team.
Arsenal, meanwhile, will face Slavia Prague, who have already eliminated Leicester and Rangers from this season's competition.
Arsenal made it through the round of 16 relatively unscathed against Olympiacos while Paul Pogba fired Manchester United to a win over AC Milan at San Siro that booked their place in the business end of the tournament.
A semi-final against either Ajax or Roma promises to deliver one of the biggest games of the tournament so far, with the Dutch and Italian giants due to fight out their quarter-final first leg in Amsterdam.
Ajax swept Young Boys aside 5-0 on aggregate in the last 16, while Roma had a similarly comfortable win over Shakhtar Donetsk, adding to their 3-0 first leg victory with a 2-1 win in Ukraine.
The other quarter-final tie sees Spurs' conquerers Dinamo Zagreb take on Villarreal, with the winner poised to face either Arsenal or Slavia in the semi-final.
Arsenal and Manchester United being drawn in separate sides of the tree means an all-Premier League final in Gdansk is a possibility provided both sides win their next two ties.
2020/21 UEFA Europa League quarter-final draw
Granada vs Manchester United
Arsenal vs Slavia Prague
Ajax vs Roma
Dinamo Zagreb vs Villarreal
2020/21 UEFA Europa League semi-final draw
Granada or Manchester United vs Ajax or Roma
Dinamo Zagreb or Villarreal vs Arsenal or Slavia Prague
The quarter-final first legs are pencilled in for 8 April, with the second legs coming a week later on 15 April to decide the semi-finalists.
The first legs of the semi-finals are then due to take place on 29 April, ahead of the second legs on 6 May.
The final will then be hosted on Wednesday 26 May in Gdansk, three days before this year's Champions League final.
Source : 90min