Chelsea's reward for failing to defend the UEFA Champions League title is being drawn to play Sparta Prague in the last 32 of the second-tier UEFA Europa League.
Zenit St Petersburg, the 2008 UEFA Cup winner, will face Liverpool, and Tottenham Hotspur will play Lyon.
Defending champion Atletico Madrid, which beat Chelsea in the Super Cup in August, was paired with Rubin Kazan.
Three-time winner Inter Milan will play Cluj, and Ajax plays Steaua Bucharest in a meeting of former European champions.
The draw included eight third-place teams from the Champions League groups, and 24 which advanced from Europa League groups.
First-leg matches are played on 14 February (15 February AEDT), and return games on 21 February (22 February AEDT).
UEFA also drew the last-16 pairings, putting Inter and Tottenham on course to meet again after thrilling Champions League group-stage matches two years ago. Chelsea and Ajax could meet in March if both win through their last-32 matches.
Zenit, which also started in the Champions League, is content to get an attractive opponent.
"Liverpool is one of the best European clubs. It is one of the most difficult draws but we are happy," Zenit chief executive Maxim Mitrofanov told The Associated Press.
The first leg in Russia will likely be played in around minus-10 C temperatures, though Mitrofanov played down the potential advantage.
"We are also a very technical team so we also need a good pitch," he said.
Atletico is seeking a third title in four seasons in the Europa League, which has often struggled in the shadow cast by the Champions League.
"We're happy to be champions," Atletico director Clemente Villaverde said. "I think there are very, very important teams in it. Rubin Kazan is a very difficult team."
UEFA president Michel Platini showed his support by meeting with officials from the 32 clubs, arriving after the Champions League last-16 draw ceremony was completed.
Inter ambassador Luis Figo also defended the competition, which this season offers one-sixth of the prize money paid to clubs in UEFA's signature event.
"Of course it's a prestigious competition for us," Figo told AP. "You just have to look at the teams in the competition and see it's difficult to reach the final."
The Italian club's route to the final in Amsterdam will have to go through England or France.
"Lyon are a club with many trophies and are a top team," Tottenham coach Andre Villas-Boas said. "It's a huge fixture and will fuel excitement."
Tottenham's group stage rival Lazio, which was paired with Borussia Monchengladbach, still awaits details of UEFA disciplinary charges after Italian fans directed abuse at the English club's traditional Jewish following inside the Olympic Stadium in Rome.
UEFA general secretary Gianni Infantino warned clubs to curb unsporting and racist behaviour: "Don't let it spoil the party," he told officials.
The Zenit v Liverpool matches are a likely focus for debate about racism.
Some of the Russian clubs fans this week urged the club not to sign black or gay players, while Liverpool forward Luis Suarez served an eight-match ban last season for directing racial comments at Manchester United defender Patrice Evra.
"Yes, we probably have some fans who have different opinions about racism," Mitrofanov told AP. "But we are here playing football and we are against racism. Playing in this competition will help."
UEFA Europa League Round of 32
Match 1: BATE Borisov v Fenerbahce
Match 2: Inter Milan v Cluj
Match 3: Levante v Olympiacos
Match 4: Zenit Saint-Petersburg v Liverpool
Match 5: Dynamo Kiev v Bordeaux
Match 6: Bayer Leverkusen v Benfica
Match 7: Newcastle United v Metalist Kharkiv
Match 8: Stuttgart v Genk
Match 9: Atletico Madrid v Rubin Kazan
Match 10: Ajax v Steaua Bucarest
Match 11: Basel v Dnipropetrovsk
Match 12: Anzhi Makhachkala v Hannover
Match 13: Sparta Prague v Chelsea
Match 14: Borussia Moenchengladbach v Lazio
Match 15: Tottenham Hotspur v Lyon
Match 16: Napoli v Plzen
UEFA Europa League Round of 16 (to be played on 7 and 14 March (8 and 15 March AEDT)
Winner Match 16 v Winner Match 1
Winner Match 6 v Winner Match 5
Winner Match 12 v Winner Match 7
Winner Match 8 v Winner Match 14
Winner Match 15 v Winner Match 2
Winner Match 3 v Winner Match 9
Winner Match 11 v Winner Match 4
Winner Match 10 v Winner Match 13
UEFA Europa League
Valencia booked its place in the semi-finals of the UEFA Europa League with a remarkable comeback to beat Basel 5-0.