Friday's Europa League draw produced other mouthwatering ties.
Bookmakers' favourites Borussia Dortmund were handed a tricky route into the last eight against Tottenham Hotspur, second in the Premier League behind Leicester City.
Holders Sevilla, chasing a third successive title, will play Basel, while Valencia, who have enjoyed a recent resurgence by winning their last four games under English coach Gary Neville, face an all-Spanish tie against Athletic Bilbao.
Liverpool and United first played each other more than 120 years ago, but they have never faced off in European competition, adding an extra dimension to what past experience suggests is likely to be a feisty encounter.
United hold the upper hand in recent meetings and have completed back-to-back league doubles over their rivals, with Liverpool yet to record a victory against United manager Louis van Gaal.
“It’s great," Liverpool's German boss Juergen Klopp told reporters following the draw. "We deserve these games. It’s not easy. I told my staff yesterday that I wanted Man United."
For Liverpool and United the competition has taken on added significance with both having slipped off the pace in the chase for a place in the Premier League's top four, which would secure qualification for the Champions League.
Since last season, the winners of the Europa League have been handed a back-door pass into the continent's elite competition.
Ukrainian outfit Shakhtar Donetsk were drawn against Belgian side Anderlecht, Villarreal will face Bayer Leverkusen, Sparta Prague will play Lazio and Fenerbahce take on Braga.
The two-legged ties will be played March 10 and 17.
(Reporting by Toby Davis, editing by Ed Osmond and John Stonestreet)
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