It will be the second time new Toffees boss Sam Allardyce leads the club into their most important game, with the Reds also set to host Everton in the Premier League this month.
That tie is not the only grudge match that came out of the hat as Premier League and Championship teams entered the national competition, with Crystal Palace set to visit Brighton and Middlesbrough facing Sunderland.
Arsenal face a trip to second-tier club Nottingham Forest, while Forest’s Midlands rivals Derby County also landed a plum draw away to Manchester United.
Tottenham will be at home to League One outfit AFC Wimbledon and Manchester City face a stern test in Premier League overachievers Burnley.
Chelsea, one of the last teams to be drawn, were handed an away match at Championship club Norwich City.
Hereford, who were one of the lowest-ranked teams in the second round, will be rewarded with a home tie against Leicester City if they can come through a replay against Fleetwood Town.
Slough, who play at the same level of the English pyramid, face Rochdale on Monday night with a trip to Doncaster Rovers waiting for the winner.
League Two side Luton Town can look forward to a visit to St James’ Park to face Newcastle United, while Championship high-flyers Wolves will hope to upset struggling Swansea City.
The third-round ties will be played on the weekend commencing January 5, with broadcast details to follow.
Arsenal are the defending FA Cup champions and have won the competition in three of the past four years, with Manchester United interrupting their recent dominance in 2015-16.
Those wins have made the Gunners the most successful team in FA Cup history, with 13 wins - one ahead of United and five ahead of third-placed Tottenham.
