Liverpool have been drawn against Russian side Zenit St Petersburg in the last 32 of the Europa League.
Fellow English side Newcastle will play Metalist Kharkiv of Ukraine, while Chelsea face Czech team Sparta Prague and Tottenham take on Lyon of France.
Defending champions Atletico Madrid of Spain take on Russia's Rubin Kazan.
Ajax, who qualified as a third-placed team from the Champions League group stages - ahead of Manchester City - are paired with Steaua Bucharest.
The winner of that game will take on Chelsea or Sparta Prague in the last 16 - the draw for which was made immediately after the last 32 draw.
Newcastle will set up a clash with big-spending Anzhi Makhachkala of Russia or German side Hannover should they beat Kharkiv.
Magpies manager Alan Pardew admitted he knew little about the Ukrainian outfit after the draw was made.
"I do know it's a long journey, I've had a look at that," he conceded. "It's a tough draw in terms of travel. The opposition I know very little about. I can't even comment on that until such time as we do some studying."
Kharkiv play in the 40,003-capacity Metalist Stadium and last season finished third for the sixth successive campaign in the Ukrainian Premier League.
They played Everton in the 2007-08 Uefa Cup, drawing the away leg 1-1 at Goodison Park before losing the return 3-2 at home to exit the competition.
Should Tottenham beat Lyon, they will face Inter Milan or Cluj in the next round while Liverpool will play Basel or Dnipro if they beat Zenit.
Zenit supporters' group Landscrona called for non-white and gay players to be excluded from the team, claiming black players are "forced down Zenit's throat".
"I'm not surprised. Everybody knows Zenit supporters are no good and racist," Anzhi Makhachkala defender Christopher Samba told BBC Radio 5 live.
Liverpool secured their place in the last 32 by winning Group A ahead of Anzhi, while Newcastle and Tottenham came second in Group D and J respectively.
Chelsea qualified by finishing third in their Champions League group behind Juventus and Shakhtar Donetsk.
The first legs of the last 32 will be played on Thursday, 14 February, with the return fixtures the following week on 21 February.
The last 16 first legs will be played on Thursday 7 March, with the return games the following week on 14 March.
Europa League last-32 draw:
BATE Borisov v Fenerbahce
Inter Milan v Cluj
Levante v Olympiakos
Zenit St Petersburg v Liverpool
Dynamo Kiev v FC Bordeaux
Bayer Leverkusen v Benfica
Newcastle v FC Metalist Kharkiv
Stuttgart v Genk
Atletico Madrid v Rubin Kazan
Ajax v Steaua Bucharest
FC Basel v Dnipro
Anzhi Makhachkala v Hannover
Sparta Prague v Chelsea
Borussia Monchengladbach v Lazio
Tottenham v Lyon
Napoli v Plzen
Napoli or Viktoria Plzen v BATE Borisov or Fenerbache
Leverkusen or Benfica v Dynamo Kiev or Bordeaux
Anzhi Makhachkala or Hannover v Newcastle or Metalist Kharkiv
Stuttgart or Genk v Monchengladbach or Lazio
Tottenham or Lyon v Inter Milan or Cluj
Levante or Olympiakos v Atletico Madrid or Rubin Kazan
Basel or Dnipro v Zenit St Petersburg or Liverpool
Ajax or Steaua Bucharest v Sparta Prague or Chelsea