The open draw allowed for teams from the same nation to be paired together and sees Manchester United and Liverpool pitted against one another for the first time in European competition.
United came from behind to progress past Midtjylland in the last round, while Liverpool saw off Augsburg 1-0 on aggregate.
Having lost to their arch-rivals in his first match against them at Anfield in January despite dominating the game, Liverpool manager Jurgen Klopp is looking to exact revenge over two legs next month.
“It’s great. We deserve these games,” Klopp said.
“Obviously it is not easy but you can ask my staff but when they asked me yesterday who I wanted, I said ‘Man United’.
“I think we have to clear something. We had a good game when we lost 1-0 but it was not what we deserved.
“It gives us a chance to make it better and that is what we will try to do.”
Klopp, who is preparing his side for the League Cup final against Manchester City at Wembley, admitted there were no comfortable options in the draw.
“There were no easy games in this round so there was no chance for an easy game. Man United – cool,” he added.
“With the draw today it seems like it is Liverpool against Manchester – like always – but now in really important games.”
Tournament favorites Borussia Dortmund have been dealt a tricky tie against another Engligh club in the form of Tottenham, while defending champions Sevilla face off against final hosts Basel.
Gary Neville avoided being drawn against his former club and is tasked with preparing his Valencia side for a two-legged clash with Athletic Bilbao, and Villarreal meet Bayer Leverkusen in another mouthwatering tie.
Elsewhere, Shakhtar Donetsk face Anderlecht, Sparta Prague meet Lazio, and Fenerbahce have been drawn against Braga.
Draw in full:
Shakhtar Donetsk v Anderlecht
Basel v Sevilla
Villarreal v Bayer Leverkusen
Athletic Bilbao v Valencia
Liverpool v Manchester United
Sparta Prague v Lazio
Borussia Dortmund v Tottenham
Fenerbahce v Braga
The first legs will be played on 11 March with the returns on 18 March (AEDT).