Louis Van Gaal’s side will host Liverpool at Old Trafford on March 10, with the return leg at Anfield on March 17.
United and Liverpool have never met in a European competition. The Red Devils completed back-to-back league doubles over Jurgen Klopp’s side in the Premier League this season.
“It’s great,” Klopp told reporters following the draw. “We deserve these games. It’s not easy. I told my staff yesterday that I wanted Man United.”
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Meanwhile, Tottenham were drawn against Borussia Dortmund.
Defending champions, Sevilla, will play Basel, while Valencia, face an all-Spanish tie against Athletic Bilbao.
In the other draws, Shakhtar Donetsk will face Belgian side Anderlecht, Villarreal will slog it out with Bayer Leverkusen, Sparta Prague will play Lazio and Fenerbahce take on Braga.
The two-legged ties will be played March 10 and 17.