Gareth Taylor's side travel to the Spanish capital for the first leg of our showdown with Las Blancas, which will take place on Tuesday 31 August with kick-off scheduled for 21:00 (CET).
The return clash then takes place at the Academy Stadium on Wednesday 8 September, with the match getting underway at 19:00 (UK).
The overall victors will be decided by an aggregate score taken across the two fixtures but, if it remain level, then extra time and a penalty shootout will be used to separate the two sides.
A spot in the 16-team group stages of this season's revamped competition is up for grabs, which replaces the knockout Round of 16.
The top two in each of the four groups will progress to the quarter-finals, the stage at which Gareth Taylor's side were edged out by eventual winners Barcelona in last season's competition.
Madrid are taking place in their inaugural Champions League campaign, having qualified for the competition by virtue of finishing second in the Spanish league.
Holders Barcelona are already confirmed for the group stage, alongside Chelsea, Paris Saint-Germain and Bayern Munich.
They will be joined by 12 teams taking part in the Round Two ties from the respective champions and league paths, including one of City or Real Madrid.
The format ensures at least 10 nations feature in the group stage.
ROUND TWO DRAW
Sparta Praha vs Køge
Osijek vs Breidablik
Vllaznia vs Juventus
Twente vs SL Benfica
Apollon vs Kharkiv
Servette vs Glasgow City
Vålerenga vs Häcken
Levante v Lyon
Arsenal v Slavia Praha
Real Madrid v Manchester City
Wolfsburg vs Bordeaux
Rosengård vs Hoffenheim