The Manchester club defeated a 10-man Real 2-1 at the Bernabeu in the last-16 first leg in February, and the tie will be completed on either 7 or 8 August at the Etihad Stadium.
Lyon and Juventus must also complete their last-16 tie ahead of the quarter-finals, with the French club having won the first leg 1-0 at home.
Elsewhere in the quarter-finals, which take place 12-15 August, the winner of Napoli vs Barcelona will face the winner of Chelsea vs Bayern Munich. The first leg of the former fixture ended 1-1 in Italy, while Bayern cruised to a 3-0 victory over Chelsea at Stamford Bridge. Both first legs saw players sent off – Arturo Vidal late on for Barca, and Marcos Alonso in the final 10 minutes moments for Frank Lampard’s side.
In the remaining quarter-final, Atalanta from Serie A take on French champions Paris Saint-Germain.
A draw was also made for the semi-finals.
Here is the full quarter-final draw:
Real Madrid / Manchester City vs Lyon / Juventus
RB Leipzig vs Atletico Madrid
Napoli / Barcelona vs Chelsea / Bayern Munich
Atalanta vs Paris Saint-Germain
Real Madrid / Man City / Lyon / Juventus vs Napoli / Barcelona / Chelsea / Bayern Munich
RB Leipzig / Atletico Madrid vs Atalanta / PSG