It would also match Blackburn's achievement of three successive Cup wins in the 1880s and Manchester United's overall record of 10 Cup successes.
Seeking to extend their own record, United have been drawn at home against neighbours Manchester City or Tottenham. The sides replay next Wednesday.
In other games, West Ham face another trip to a Premiership club after beating Wolves yesterday as they will take on the winners of Fulham's replay with Everton.
If Chris Coleman's side come through that tie, they will face the Hammers for the first time in the FA Cup since the 1975 final which they lost 2-0.
Telford United, the only non-Leaguers left in the competition, have been handed a home clash with Burnley but they must first overcome Millwall in their rearranged tie next Wednesday. Liverpool face Portsmouth at Anfield.