Premier League's Leicester City will take on PSV Eindhoven, while French side Marseille was pitted against Greece's PAOK in the Europa Conference League draw held Friday.
The Foxes face former European champion PSV with a possible semifinal against Jose Mourinho's Roma in store for the winner.
The Premier League side made it through to the second European quarterfinal of its history by defeating French club Rennes 3-2 on aggregate Thursday.
Brendan Rodgers's team will be at home in the first leg on April 7 before going to the Netherlands for the return a week later.
PSV, who won the European Cup in 1988 and the UEFA Cup in 1978, crushed FC Copenhagen 8-4 on aggregate in the last 16 and currently sit second in the Dutch league, two points behind leaders Ajax.
The winners of that tie will face either Roma or Bodo/Glimt in the semifinals, with the Italians meeting the Norwegians again after the sides also clashed in the group stage.
The Norwegian champion trounced Roma 6-1 at home and then drew 2-2 in Rome. It has since eliminated Celtic and AZ Alkmaar in the knockout stages.
The quarterfinal draw also saw former Champions League winner Marseille paired with PAOK of Greece, while Feyenoord – another past European Cup winner – will play Slavia Prague.
The final of the new third-tier continental competition will be played in the Albanian capital, Tirana, on May 25.
