The Rams won at Arsenal in the previous round, are unbeaten in their last five games and include first-team starlets Mason Bennett and Will Hughes in their ranks. Both youngsters have been drafted into this week's England Under-17 squad.
Coach Darren Wassall told Derby Player: "To get United away is a dream for a lot of the players. Over the course of their lives, Manchester United have been at the top of the tree in terms of the Premier League, youth team and Reserves, and so to have to go and play them at Under-18 level is great for all of them.
"We know it's a very difficult task playing against a team that has produced youth team players throughout their history to grace the Premier League and Champions League. We thoroughly respect the opposition but hope to replicate the form we showed against Arsenal."
Paul McGuinness' side disposed of Torquay United 4-0 in the third round although one of the scorers that night, Tom Lawrence, picked up an injury and missed the 3-3 draw against Bolton in the only fixture to survive the weather this year.
The victors on the evening, following extra-time and penalties if required, will face a trip to either Portsmouth or Swansea in the fifth round.