Sixth-tier Maidstone United will face either Sheffield Wednesday or Coventry in the FA Cup fifth round.
Holders Manchester City will travel to fellow Premier League side Luton Town.
Fifth-round ties are to be played during the week commencing 26 February.
Maidstone make history
Goals from Lamar Reynolds and Sam Corne shocked Ipswich, as the Stones became the first side from National League North or South to reach the last 16 of the FA Cup since the regional split was introduced in 2004.
Maidstone have also eliminated Steyning Town, Winchester City, Torquay, Chesham, Barrow and Stevenage from the FA Cup on their way to the fifth round.
The competition is hotting up
The draw was made at half-time in Liverpool’s fourth-round tie against Championship side Norwich City.
Jurgen Klopp on Friday announced his intention to leave the Reds at the end of the campaign and, should they overcome the Canaries at Anfield, Liverpool will host either Watford or Southampton.
Elsewhere, there is an all-Premier League tie between Wolves and Brighton, while Newcastle will travel to either Blackburn Rovers or Wrexham.
League Two side Newport County were in the hat for the fifth round, as they meet Manchester United at Rodney Parade on Sunday afternoon (16:30 GMT). Whoever wins that tie will have a trip to either Bristol City or Nottingham Forest.
FA Cup fifth-round draw in full
Blackburn Rovers or Wrexham v Newcastle United
Chelsea or Aston Villa v Leeds United or Plymouth Argyle
Bournemouth v Leicester City
Liverpool or Norwich v Watford or Southampton
Bristol City or Nottingham Forest v Newport County or Manchester United
Wolverhampton Wanderers v Brighton & Hove Albion
Sheffield Wednesday or Coventry City v Maidstone United
Luton Town v Manchester City