Both Real and City failed to advance automatically to the last-16 as one of the top eight sides after they finished 11th and 22nd, respectively, in the new league-phase format.
Teams that finished ninth to 24th will compete in a two-legged playoff to advance to the last 16.
Real and City have played each other in four knock-out ties since 2020 and will be facing off for a fourth consecutive year.Â
The Spanish league leaders will fancy their chances having eliminated English clubs in the knock-out stages 13 times.
Although City thrashed the Spanish club 5-1 on aggregate in the semi-finals in 2023 en route to the treble, Real exacted revenge last year when they beat Pep Guardiola's side on penalties in the quarter-finals after two draws.
The competition does not get any easier for either team as they will face either Atletico Madrid or Bayer Leverkusen in the last 16.
With teams from the same country also allowed to face each other, unlike in previous years, the play-offs will have an all-French tie with Paris St Germain facing Brest. The winners will face either Liverpool or Barcelona in the last 16.
Juventus and AC Milan avoided each other in the draw, with the two Serie A sides facing Dutch clubs PSV Eindhoven and Feyenoord, respectively.
However, the Italian sides may face Inter Milan if they advance to the next round or they could come up against Arsenal.
Last year's runners-up Borussia Dortmund take on Portuguese side Sporting while Club Brugge face Atalanta.
CHAMPIONS LEAGUE KNOCKOUT PLAYOFFS DRAW
Club Brugge v Atalanta
Sporting v Borussia Dortmund
Manchester City v Real Madrid
Celtic v Bayern Munich
Juventus v PSV Eindhoven
Feyenoord v AC Milan
Brest v Paris St Germain
AS Monaco v Benfica
(Team mentioned second plays second leg at home - play-off first leg: February 11/12, second leg February 18/19.
