Hartlepool have already claimed the scalp of Premiership long-ball merchants Stoke City with a 2-0 win in the third round and will be looking forward to another home game against Premiership opposition after the Hammers 3-0 victory over Barnsley on Saturday.
Full FA Cup draw:
Liverpool
Southampton or Manchester United v Tottenham Hotspur
Hartlepool United v West Ham Unitted
Leyton Orient or Sheffield United v Charlton Athletic or
Chelsea or Southend United v
West Bromwich Albion or Peterborough United v Queen's Park Rangers or
Torquay United v
Watford v Leicester City or Crystal Palace