This will be the 23rd time Liverpool have played Everton in the FA Cup, with their last meeting coming in a semi-final win in 2012.
It will be the second Merseyside derby of the season as the Reds play Everton this Sunday in the Premier League.
Liverpool are currently 4th in the league following a 1–5 demolition of Brighton at the weekend.
Everton are 10th, with new manager Sam Allardyce winning his first game in charge, a 2-0 victory against Huddersfield.
Who can forget the eight-goal thriller between Reds and the Toffees in 1991’s FA Cup fifth-round replay, which proved to be the final match of Kenny Dalglish’s first tenure as Liverpool manager.
Elsewhere in the draw holders Arsenal will travel to Nottingham Forest.
Manchester City have a home tie against Burnley, while Manchester United host Derby and Chelsea are away at Norwich.
Non league AFC Fylde will take on Premier League side Bournemouth if they beat Wigan in a replay.
AFC Wimbledon will travel to Wembley to take on Tottenham.
Ties to be played on January 5-8.