The Reds drew 1-1 with the Toffees at home in the Premier League on December 10 and both sides will be eager to avoid a repeat result, which would necessitate a replay.
Read on for a closer look at the two sides ahead of the clash, but first here are the viewing details you need to catch the action:
Date: Friday, January 5
Time: 7:55 p.m. GMT/2:55 p.m. ET
TV: BBC One (UK), Fox Soccer 1 USA
Liverpool come into the tie in strong form having won their last three matches, which included a 5-0 thrashing of Swansea City on Boxing Day followed by a 2-1 comeback win over Leicester City and a victory by the same scoreline at Burnley.
The Guardian's Sachin Nakrani hailed their recent showings:
So, too, did Goal's Melissa Reddy, who noted the impressive unbeaten run the Reds are on:
Liverpool have not lost a match since the 4-1 defeat to Tottenham Hotspur on October 22.
By contrast, the Toffees' recent form has left much to be desired after they initially made a strong start to life under Sam Allardyce.
Bleacher Report's Matt Jones was unhappy with their approach against the Red Devils on Monday:
The Toffees could raise their game somewhat against their local rivals, but it does not bode well for them heading into the Anfield clash.
What could play into their hands is the ongoing speculation over Philippe Coutinho's future. The Brazilian has been linked with a move to Barcelona and will not feature in the Merseyside derby, according to Sky Sports' Guillem Balague:
Guillem Balague @GuillemBalague
Coutinho will not be “fit” for the the FA Cup game on Friday vs Everton. On future: LFC’s tone has changed -it seems they are open to all the options. Sell now, sell now for the summer. Keeping him beyond then seems the very last option. But no offer from FBC has arrived... yet https://t.co/rFGyFuXqzF
His absence deprives the Reds of one of their chief creators, and the transfer saga also presents an unwelcome distraction others may look to capitalise on.
Liverpool will need to be able to put that aside during the match or they run the risk of an early cup exit at the hands of their local rivals.