The two heavyweights have already crossed swords once this campaign, with City mounting a comeback to beat the record 15-times European champions Madrid 2-1 in December's group stage match.
"We played against each other already in the group phase, so it'll be a really nice game to watch. It's like a final, we are happy to go there again," City's director of football Hugo Viana told UEFA on Friday.
Holders Paris St Germain will face Chelsea in a repeat of last year's ill-tempered Club World Cup final in which the Premier League side came out on top.
"We've played them quite a few times. They are the reigning champions but people will probably refer to what happened in the summer at the Club World Cup. It'll be tough but it holds no fear for us," Chelsea's director of football David Barnard said.
Arsenal play Bayer Leverkusen and the Premier League leaders have avoided the tournament's heavyweights after their perfect record of eight wins put them top of the standings in the league phase.
Should they qualify for the quarter-finals, Arsenal will play either Sporting or Bodo/Glimt while Real Madrid, Manchester City, PSG, Liverpool, Bayern Munich and Chelsea are on the other side of the draw.
Bayern Munich, who were second in the group stage, play Atalanta, who knocked out German side Borussia Dortmund in the playoffs thanks to a stoppage-time penalty and are the only Italian side left in the draw.
Newcastle United face Barcelona again after the Spanish side won their group-stage opener and Liverpool have been paired with Galatasaray.
Premier League strugglers Tottenham Hotspur face Atletico Madrid while Norwegian upstarts Bodo/Glimt -- who have beaten City, Atletico and Inter Milan this season -- take on Portugal's Sporting Lisbon.
LAST-16 DRAW
Real Madrid v Manchester City
Bodo/Glimt v Sporting
Paris St Germain v Chelsea
Newcastle United v Barcelona
Galatasaray v Liverpool
Atletico Madrid v Tottenham Hotspur
Atalanta v Bayern Munich
Bayer Leverkusen v Arsenal
QUARTER-FINALS
QF1: PSG/Chelsea v Galatasaray/Liverpool
QF2: Real Madrid/Man City v Atalanta/Bayern
QF3: Newcastle/Barcelona v Atletico/Tottenham
QF4: Bodo/Sporting v Leverkusen/Arsenal
SEMI-FINALS
Semi-final 1: QF1 winners v QF2 winners
Semi-final 2: QF3 winners v QF4 winners
FIRST AND SECOND LEG DATES
Last 16: March 10-11 and March 17-18
Quarter-finals: April 7-8 and April 14-15
Semi-finals: April 28-29 and May 5-6
Final: May 30 in Budapest's Puskas Arena
