The Reds booked their place in the next stage of the competition by beating Lincoln City 7-2 on Thursday.
Their reward is a meeting with the Gunners at Anfield, with Mikel Arteta's team having defeated Leicester City in their third-round match.
Fourth-round ties are scheduled to be played in the week commencing September 28. Full fixture details will be announced on Liverpoolfc.com in due course.