Holders Arsenal's first challenge is away trip to second tier Nottingham Forest and Manchester City face Burnley
FA Cup draw: Klopp takes on rival Allardyce as Liverpool host Everton
Liverpool will host city rivals Everton for the second time inside a month when they face off in the third round of the FA Cup in early January after the draw was made on Monday.
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.
Looking back on longest FA Cup tie
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 City.
Several Premier League sides could fall prey to giant killing exploits.
Inconsistent Southampton travel to Fulham, and struggling West Ham United and Swansea City are away at third tier highflyers Shrewsbury and Championship leaders Wolverhampton Wanderers respectively.
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