The Foxes, who overcame Danish side Randers in the knockout round play-offs earlier this year, were 3-2 winners on aggregate against Rennes in the last-16. Although losing the second leg 2-1 in France, Wesley Fofana's goal was ultimately enough to put City's name in the hat.
Ahead of the draw, here's all you need to know...
When does it take place?
The draw for the quarter-finals will be held at the House of European Football in Nyon, Switzerland at 2pm GMT on Friday. Leicester fans can keep updated by following @LCFC on social media and checking back to LCFC.com after the draw is complete.
Which teams could City face?
The Foxes could be paired with any of the seven other teams who also enjoyed success in the round of 16.
Bodø/Glimt
Feyenoord
Marseille
PAOK
PSV Eindhoven
Roma
Slavia Prague
There are no seedings or country protection. Any restrictions will be announced ahead of the draw.
When will the games happen?
The first leg ties will occur on Thursday 7 April, before the second legs take place on Thursday 14 April.
What else is happening?
A draw will also be conducted for the competition's semi-finals. Quarter-final ties will be numbered one to four for the semi-final draw that follows.