Liverpool, who beat Norwich City 2-1 in Wednesday's fifth-round tie at Anfield, will discover their last-eight opponents from around 7.45pm GMT on Thursday.
The quarter-final draw will take place live on ITV in the UK ahead of the meeting between Everton and Boreham Wood in round five.
It can also be followed on the official FA Cup Twitter and Facebook accounts.
The Reds will be ball number four in the draw.
Quarter-finals are scheduled to be played between Friday March 18 and Monday March 21.