Premier League leaders Arsenal, who topped the Champions League table with a perfect record, will face German side Bayer Leverkusen.
Six-time winners Liverpool will take on Galatasaray, while Tottenham have been handed a tie against Atletico Madrid.
The last-16 first legs take place on March 10 and 11, with the second legs scheduled for March 17 and 18. The schedule is expected to be released on Friday night.
If Manchester City progress past Real Madrid, they will face either Bayern Munich or Atalanta in the quarter-finals, while Chelsea and Liverpool will meet in the last eight if they knock out PSG and Galatasaray, respectively.
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