Zenit to face AEL Limassol in Champions League
Zenit made the round of 16 last season before bowing out to Borussia Dortmund 5-4 on aggregate, while Cypriot side AEL reached the group stage in 2012-13.
Copenhagen finished bottom of Group B last term and will face Dnipro Dnipropetrovsk while Red Bull Salzburg - who made the final 16 of the Europa League - will face Valletta or Qarabag.
Feyenoord's first European test of the post-Ronald Koeman era will see them take on Turkish Super Lig club Besiktas.
Scottish champions Celtic could face a relatively nearby fixture provided they can see off KR at Celtic Park.
Ronny Deila's men secured a one-goal advantage in Reykjavik and will meet Legia Warsaw or Dublin-based St Patrick's Athletic in the next round if they see the tie through.
Lille's reward for a third-place finish in the French top flight last term is a fixture with Grasshoppers of Switzerland while Standard Liege will welcome Panathinaikos of Greece for the first leg of their tie.
If Maccabi Tel-Aviv get past Santa Coloma they will likely lose home advantage for their tie with Zrinjski or Maribor.
UEFA ruled on Thursday that, due to the "current security situation in Israel", no UEFA competition matches would be played in the country until further notice.
Draw in full (Champions Route): Limassol v Zenit, Dnipro Dnipropetrovsk v Copenhagen, Feyenoord v Besiktas, Grasshoppers v Lille, Standard Liege v Panathanaikos, Valletta or Qarabag v Red Bull Salzburg, Cliftonville or Debrecen v BATE Borisov or KC Skenderbeu, Slovan Bratislava or The New Saints v Sheriff or Sutjeska, Aalborg v Dinamo Zagreb or Zalgiris, Legia Warsaw or Saint Patrick's Athletic v KR or Celtic, Dinamo Tbilisi or Aktobe v Stromsgodset or Steaua Bucharest, Zrinjski or Maribor v Santa Coloma or Maccabi Tel-Aviv, Rabotnicki or HJK Helsinki v APOEL, Sparta Prague or Levadia Tallin v Malmo or Ventspils, Ludogorets or F91 Dudelange v Partizan or HB Torshavn