Klopp spent seven years as Dortmund coach, helping the team win two German league titles and reach the Champions League final, before stepping down in 2015. He was hired by Liverpool in October.Asked after Liverpool's win over Manchester United about whether he wanted to come up against Dortmund next, Klopp said: "Why should I want the strongest team in the tournament? But if we go there, we try to win."
The teams were chosen to face each other in Friday's draw.
Sevilla, seeking a third straight Europa League title, will face Athletic Bilbao in an all-Spanish contest. Sevilla has won the UEFA Cup-Europa League in four of the last 10 seasons.
Villarreal, the third Spanish team in the quarterfinals, will play Sparta Prague while Braga will take on Shakhtar Donetsk.
The first legs will be played on April 7, with the second legs on April 14.
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