Chelsea will face holders Real Madrid in the Champions League quarter-finals.
Pep Guardiola faces his former club as Manchester City play six-time winners Bayern Munich.
Inter Milan face Benfica and Serie A champions AC Milan take on current leaders Napoli.
If Chelsea and Manchester City get through, they will meet in an all-Premier League semi-final while AC Milan or Napoli will face Inter Milan or Benfica in the other semi-final.
The first legs of the quarter-finals take place on 11-12 April, with the return games on 18-19 April.
The first legs of the semi-finals will be on 9-10 May, and the second legs on 16-17 May.
The Ataturk Olympic Stadium in Istanbul, Turkey, will host the final on 10 June.
It is the third successive season Chelsea and Real Madrid, the record 14-time winners, have met in the competition.
Chelsea beat Real in the semi-finals on their way to winning the trophy in 2020-21 before losing 5-4 on aggregate to the Spanish giants last season in the quarter-finals.
Manchester City and Bayern Munich have not met competitively since 2014 when Guardiola was in charge of the German club.
Manchester United will meet record six-time winners Sevilla in the quarter-finals of the Europa League.
Should they advance, Erik ten Hag’s side will face either Juventus – whose squad includes former United midfielder Paul Pogba – or Arsenal’s conquerors Sporting Lisbon in the semi-finals.
In the other last-eight ties, Roma face Feyenoord and Bayer Leverkusen meet Union Saint-Gilloise.
The first legs take place on 13 April, with the return games on 20 April.
Sevilla are recent serial winners of this competition, having won all of their six titles since 2006 and they defeated the Red Devils in the semi-finals on their way to winning it in 2020.
Their squad includes Brazil defender Alex Telles, who is on loan from United.
“Sevilla are very experienced in the Europa League and have won it so many times,” said United boss Ten Hag.
“We have to be aware of it.”
Ten Hag’s side, who won last month’s Carabao Cup, are also still in the FA Cup and host Fulham in the quarter-finals of that competition on Sunday
Champions League quarter-final draw
Real Madrid v Chelsea
Inter Milan v Benfica
Manchester City v Bayern Munich
AC Milan v Napoli
Champions League semi-final draw
AC Milan or Napoli v Benfica or Inter Milan
Real Madrid or Chelsea v Manchester City or Bayern Munich
Europa League quarter-final draw
Manchester United v Sevilla
Juventus v Sporting Lisbon
Bayer Leverkusen v Union Saint-Gilloise
Feyenoord v Roma
Europa League semi-final draw
Juventus or Sporting Lisbon v Manchester United or Sevilla
Feyenoord or Roma v Bayer Leverkusen or Union Saint-Gilloise