Steven Gerrard's side, who remain unbeaten this season, secured their place in the draw for the next stage of the competition with a 5-1 victory over Hartlepool United on Wednesday night.
No date or venue has yet been set for the clash with the Gunners, but the tie must be played by January 20, 2018.
LFCTV GO: Watch highlights from the 5-1 win at Hartlepool United