The pair join fellow Premier League sides Liverpool and Tottenham in Friday’s draw in Nyon, Switzerland, where the route to the Madrid finale will be decided.
There is no seeding or country protection at this stage, but UEFA has announced that United will have to reverse their fixture if drawn at home in the same week as rivals City.
“Manchester City and Manchester United will not be able to play at home on the same night, nor on consecutive nights, following a decision made by the relevant local authorities,” UEFA said.
“Therefore, should both clubs be drawn at home in the same week, the team having finished lower in the domestic league the previous season – in this case Manchester United – will be reversed in accordance with the UEFA Club Competitions Committee principles.
“Any potential reversal for the semi-finals, for the same reason, would be confirmed after the quarter-finals.”
Barcelona, Juventus, Ajax and Porto complete the Champions League quarter-final draw.