"I think Barcelona will be very concerned that they have drawn us," City coach Manuel Pellegrini, who spent the past nine seasons in the Spanish league, said after Monday's draw. "They are not the team of two years ago."
Chelsea will have an emotional reunion with Didier Drogba, its former star forward, when it plays Galatasaray. Defending champion Bayern Munich was paired with Arsenal in the round of 16 for the second straight year.
"I'm the luckiest man in this competition in both games I'll be playing home," Drogba, who spent eight seasons at Stamford Bridge, wrote on his Instagram account.
Both City and Arsenal ended up with tough draws after finishing second in their Champions League groups.
"No one of the (seeded teams) wanted to find Man City or Arsenal," said former Barcelona playmaker Luis Figo, who helped conduct the draw. "It's bad luck for Barcelona and Bayern Munich."
Nine-time champion Real Madrid faces Schalke, Manchester United drew against Olympiakos, Borussia Dortmund plays Zenit St. Petersburg, AC Milan meets Atletico Madrid and Paris Saint-Germain goes against Bayer Leverkusen.
The first legs will be played from Feb. 18-26, with the return matches set for March 11-19.
Man City is the only newcomer to the Champions League knockout rounds, and wasted an opportunity to be seeded when Pelligrini did not realize that one more goal in its 3-2 win in Munich last week would have won the group ahead of Bayern.
Manchester City's director of football is Txiki Begiristain, who joined the English club from Barcelona, and its roster includes several players from Spain's national team.
"If you want to be champions you need to beat the best ones," Begiristain said. "We have to score in away games in the Champions League."
Chelsea coach Jose Mourinho said last week that Drogba should return to his former club. The Ivorian forward's last kick as a Chelsea player was the penalty shootout winner in the 2012 final against Bayern.
The German champions have a re-match with Arsenal, which won 2-0 in Munich last season after Bayern had cruised to a 3-1 win in London.
Bayern coach Pep Guardiola also renews rivalries after his Barcelona team eliminated Arsenal in 2010 and '11.
"I know Arsene Wenger quite well, I know his players quite well," Guardiola said at the Club World Cup in Morocco. "In the draw, it was the most difficult team."
Madrid continues its quest for a record 10th European title with a relatively low-key pairing against Schalke.
"On paper, yes, but that is only theory," Real Madrid director Emilio Butragueno said. "Football is unpredictable. It's a German team with a great mentality."
Dortmund, which lost to Bayern in last season's final, got arguably the most unwanted trip — a Feb. 25 visit to Russia to play Zenit in almost certain below-freezing temperatures.
"It won't be easy," Dortmund chief executive Hans-Joachim Watzke said. "But when I look at the teams the other German clubs have to play against, we got through OK."
Leverkusen will be at home first against big-spending PSG and its forward line of Zlatan Ibrahimovic and Edinson Cavani.
"You don't have to be an expert to say we are the outsiders," said Leverkusen sporting director Rudi Voeller, whose team lost 5-0 at home to United last month.
PSG coach Laurent Blanc said it "could have been worse," but then added: "If they are second to Bayern it means they are a talented team."
AP Sports Writer Paul Logothetis in Agadir, Morocco, contributed to this report.
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