The all-Merseyside fixture will see the newly-installed Everton manager, Sam Allardyce, visit Anfield for the second time in the space of a month with the teams set to collide in the Premier League on Sunday afternoon.
The FA Cup third round draw is complete.
One intriguing tie sees Middlesbrough play host to Sunderland in a Tees-Wear derby, while the only other Yorkshire side at home are Doncaster Rovers, who will welcome the winners of tonight's tie between Slough and Rochdale.
Swansea City, bottom of the Premier League, face Championship leaders Wolves at Molineux. Another eye-catching all-Premier League duel pits together rivals Brighton and Crystal Palace, while the North East duo of Middlesbrough and Sunderland face-off at the Riverside. The holders, Arsenal, will face what could be a testing encounter with Nottingham Forest at the City Ground.
They will go to Premier League AFC Bournemouth if they can win at the DW Stadium.
Everton did eliminate the Reds from the tournament in 2009 when Dan Gosling scored the only goal of the game to settle a fourth round replay between sides.
Third round ties are due to take place over the weekend of January 6, with matches selected for television coverage to be announced in due course.