Maidstone will face Championship opposition and Chelsea could host Leeds United in the Fifth Round of the FA Cup.
With several ties needing replays the draw went ahead on Sunday evening.
Non-League Maidstone have been drawn away to Sheffield Wednesday or Coventry City.
FA Cup Fifth Round Draw:
Blackburn Rovers or Wrexham v Newcastle United
Chelsea or Aston Villa v Leeds United or Plymouth Argyle
Bournemouth v Leicester City
Liverpool v Watford or Southampton
Bristol City or Nottingham Forest v Manchester United
Wolverhampton Wanderers v Brighton & Hove Albion
Sheffield Wednesday or Coventry City v Maidstone United
Luton Town v Manchester City