Jürgen Klopp’s team were paired with the Portuguese side during Friday’s draw at UEFA’s headquarters in Nyon, Switzerland.
The Reds will play the first leg away from home, before hosting Benfica for the second meeting.
The first legs of this season’s last-eight ties will take place on April 5/6, with return dates pencilled in for April 12/13.
Confirmed fixture and ticket details will be announced on Liverpoolfc.com in due course.
Quarter-final draw
Chelsea v Real Madrid
Manchester City v Atletico Madrid
Villarreal v Bayern Munich
Benfica v Liverpool
The winners of the tie between Liverpool and Benfica will face either Villarreal or Bayern Munich in the last four, with the first leg at home.