Liverpool face a tough test against Zenit St Petersburg while Tottenham take on Lyon in the Europa League last 32.
Newcastle United face Metalist Kharkiv and Champions League holders Chelsea take on Sparta Prague as Petr Cech returns to his former side.
Elsewhere, holders Atletico Madrid take on Rubin Kazan, Inter Milan are pitted against CFR Cluj and Ajax, whose Amsterdam Arena is being used for the final in May, play Steaua Burcuresti.
While Brendan Rodgers' Liverpool contemplate another trip to Russia in this season's campaign, Tottenham goalkeeper Hugo Lloris is set to return to Lyon, whom he left in the summer for White Hart Lane.
Spurs boss Andre Villas-Boas said: "It's not going to be an easy game for us but the boys are fresh and will be ready."
Newcastle have been rewarded for qualifying from their group with a visit to Kharkiv, who have an 100% home record in the competition and whose venue was used during Euro 2012.
Toon manager Alex Pardew said: They won their group, so it's a tough agenda for us, but we look forward to it."
Chelsea, who became the first Champions League holders to be knocked-out in the group phase, will travel to a Prague side who won just two of their group stage matches in qualifying for the knock-out phase.
Should The Blues reach the last 16, they could face Ajax, conquers of Manchester City in the Champions League, while if Tottenham are successful they could square off against Inter Milan, who they faced in Europe's premier club competition in two memorable group games in 2010.
Guus Hiddink's Anzhi Makhachkala could await Newcastle in the round of 16 should the Premier League win their tie and Liverpool will face either FC Basel or Dnipro.
The matches of the round of 32 will be played across the weeks of 14 and 21 February while the round of 16 will be played over the weeks of 7 and 14 March.
Europa League last 32 and 16 draws in full:
Napoli/Viktoria Plzen v BATE Borisov/Fenerbahce
Bayer Leverkusen/Benfica v Dynamo Kiev/Bordeaux
Anzhi Makhachkala/Hannover v Newcastle United/Metalist Kharkiv
VfB Stuttgart/Genk v Borussia Monchengladbach/Lazio
Tottenham Hotspur/Lyon v Inter Milan/CFR Cluj
Levante /Olympiakos v Atletico Madrid/Rubin Kazan
FC Basel/Dnipro v Zenit St Petersburg/Liverpool
Ajax Amsterdam/Steaua Bucuresti v Sparta Prague/Chelsea