Questions still remain over the future of Chelsea with the club due to be sold soon. Until then, it faces restrictions which could make the tie even more difficult.
Current sanctions prevent it from selling new tickets for upcoming matches until a new owner comes in and their budget for traveling to away games has also been capped.
European football’s governing body UEFA told CNN it was working with Chelsea on all aspects relating to the upcoming match.
The match itself will also throw up plenty of headlines with Eden Hazard making his return to Stamford Bridge alongside former Blues manager Carlo Ancelotti.
“The challenge cannot be much higher,” Chelsea boss Thomas Tuchel told reporters, talking about the draw.
“It’s a big challenge and there is also big excitement around this fixture. We know what is coming and it will be an exciting match and tough challenge.”
Tuchel said it would be a big disadvantage for his side if fans were not able to attend the matches.
“The game changes so much with spectators, so hopefully we find a solution,” he said.
Manchester City also faces a Spanish side in Atlético Madrid, Benfica will take on Liverpool, while Villarreal will play Bayern Munich.
The first leg of the quarterfinals will be played on April 5 and 6 with the return leg scheduled for the week after.
Teams also discovered their potential route to the final during the live draw in Nyon, Switzerland.
The winner of the Chelsea and Real Madrid quarterfinal will face either Atlético or Manchester City in the semifinals, while Benfica or Liverpool will play the winner of Villarreal and Bayern.
The final will take place in Paris on May 28 at the Stade de France after European football’s showpiece match was moved from St. Petersburg, Russia, amid the invasion of Ukraine.