Manchester United face Danish side Midtjylland in the last 32 of the Europa League after dropping out of the Champions League.
Liverpool boss Jurgen Klopp will make a return to Germany as the Reds play Augsburg.
Tottenham Hotspur have been drawn against Serie A title chasers Fiorentina for the second consecutive season at this stage.
Gary Neville's Valencia have been paired with Rapid Vienna.
The first legs are on Thursday, 18 February, with the return ties a week later.
All three English clubs will be at home for the second leg because they were seeded.
Spurs and Liverpool qualified after winning Group J and B respectively, while United finished third in Champions League Group B.
Midtjylland chairman Rasmus Ankersen said: "We have already beaten one English team so we are not afraid. We are a small club with a small budget and we know we can't outspend them so we have to out-think them and, so far, this way has worked for us in the Europa League.
"We know we have a chance and we will take up the challenge. If we can beat Southampton we can beat Manchester United and the players will feel that and believe it."
Augsburg coach Markus Weinzierl said: "The anticipation of facing Liverpool is huge. Everyone was happy.
"Liverpool are a cult club and Jurgen Klopp is a huge name in Germany so I'm happy for the whole club. We will do everything we can. This game is something special."
Draw in full
Valencia v Rapid Vienna
Fiorentina v Tottenham Hotspur
Borussia Dortmund v FC Porto
Fenerbahce v Lokomotiv Moscow
Anderlecht v Olympiakos
Midtjylland v Manchester United
Augsburg v Liverpool
Sparta Prague v Krasnodar
Galatasaray v Lazio
Sion v Braga
Shakhtar Donetsk v Schalke
Marseille v Athletic Bilbao
Sevilla v Molde
Sporting Lisbon v Bayer Leverkusen
Villarreal v Napoli
Saint-Etienne v Basel