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City's clash with Dortmund will represent in-demand forward Erling Haaland's first visit to the Etihad Stadium. The Norway international is a transfer target for several of Europe's top sides, and his father, Alf-Inge, played for City.
Madrid boss Zinedine Zidane is looking to become the first manager to win the competition on four occasions, but he will have to overcome Liverpool, whom Los Blancos beat in the 2018 final. Jurgen Klopp's side recovered to win the trophy the next season.
"We know the difficulty of the game," Zidane said of the draw. "At this stage, all the teams are really good. It will be really demanding.
"We know them, physically they'll demand a lot, but right now that's for after the international break. We can't say it's a good or a bad draw. Right now for Liverpool, they aren't up there in the table but at any time, in a knockout tie, they can play their cards.
"And you can say the same thing about us. We were on the brink and now we're still here, in two competitions. It will be a game between two teams that have won a lot of Champions League titles and it will be very diffciult, at this level it's always difficult to win."
Bayern boss Hansi Flick could become the second manager of a men's side to retain the Champions League after Zidane achieved the feat with Madrid, while PSG manager Mauricio Pochettino will be hoping to go one better, having seen his Tottenham Hotspur lose the final to Liverpool in 2019.
Thomas Tuchel, who led PSG to the final last season, will fancy his side's chances against Porto, though Chelsea should be wary after the Portuguese side overcame Juventus in the round of 16.
Chelsea and Liverpool met each other in five consecutive seasons in the Champions League from 2005 to 2009, but, should both make it to the semifinal, it would be their first encounter in the competition since.
Only two of the remaining teams are top of the table in their domestic leagues, with La Liga leaders Atletico Madrid having been knocked out in the round of 16.
City and PSG are the only sides left in the competition who have never won the Champions League, though the French side did reach the final last season and will be looking to build on that.
The quarterfinal first legs will be played on April 6/7 with the returns on April 13/14, and the first semifinals will be on April 27/28 with second legs to take place on May 4/5. The final will be played in the Turkish city of Istanbul on May 29.
Manchester City vs. Borussia Dortmund
FC Porto vs. Chelsea
Bayern Munich vs. Paris Saint-Germain
Real Madrid vs. Liverpool
Bayern Munich or Paris Saint-Germain vs. Manchester City or Borussia Dortmund
Real Madrid or Liverpool vs. FC Porto or Chelsea