Liverpool — who beat Everton in the 2012 semi-final, their last FA Cup meeting — also host their struggling neighbours in the Premier League next Sunday.
Everton have had a torrid time in the Premier League so far this season and failed to progress to the knockout stages in the Europa League, although they have the survival specialist Sam Allardyce now installed as manager.
Adding extra spice is a tense relationship between Liverpool manager Jurgen Klopp and Allardyce, with the latter making disparaging remarks about the German in the past.
Klopp, though, offered an olive branch last week, wishing Allardyce — who has brought in former Liverpool midfielder and coach Sammy Lee onto his staff — well in his new job.
Liverpool have beaten Everton on both the occasions they have met in the final in 1986 and 1989.
Their overall head to head FA Cup record has seen them clash on 23 occasions, with Liverpool winning 10, Everton seven, and six draws.
Elsewhere, holders Arsenal’s first challenge is an away trip to second tier Nottingham Forest while Premier League leaders Manchester City face a potentially tricky home tie with Burnley.
Arsenal are not the only Premier League giants to face second tier opposition with Manchester United at home to Derby County and last season’s beaten finalists Chelsea away at Norwich.
Several Premier League sides could fall prey to giant killing exploits.
Inconsistent Southampton travel to Fulham, and struggling West Ham and Swansea are away at third tier highflyers Shrewsbury and Championship leaders Wolverhampton Wanderers respectively.
Draw (Ties to be played January 5-7)
Ipswich v Sheffield United
Watford v Bristol City
Birmingham v Burton
Liverpool v Everton
Brighton v Crystal Palace
Aston Villa v Woking or Peterborough
Bournemouth v AFC Fylde or Wigan
Coventry v Stoke
Newport v Leeds
Bolton v Huddersfield
Port Vale or Yeovil v Bradford
Nottingham Forest v Arsenal
Brentford v Notts County
QPR v MK Dons
Manchester United v Derby
Forest Green or Exeter v West Brom
Doncaster v Rochdale
Tottenham v AFC Wimbledon
Middlesbrough v Sunderland
Fleetwood or Hereford v Leicester
Blackburn or Crewe v Hull
Cardiff v Mansfield
Manchester City v Burnley
Shrewsbury v West Ham
Wolves v Swansea
Stevenage v Reading
Newcastle v Luton
Millwall v Barnsley
Fulham v Southampton
Wycombe v Preston
Norwich v Chelsea
Gillingham or Carlisle v Sheffield Wednesday