The Reds were paired with the Spanish club during Friday morning’s draw for the last eight and the semi-finals in Nyon, Switzerland.
Jürgen Klopp’s side will be away from home for the first leg, before the return match takes place a week later.
Quarter-final games are scheduled to be played on April 6/7 (first legs) and April 13/14 (second legs). Full fixture details will be confirmed on Liverpoolfc.com soon.
Quarter-final draw
Manchester City v Borussia Dortmund
FC Porto v Chelsea
Bayern Munich v Paris Saint-Germain
Real Madrid v Liverpool