Butcher has placed youth at the heart of his attempts to transform Hibs with under-20s players Sam Stanton, Jordon Forster, Alex Harris and Danny Handling all starting recent games.
And they come up against some of United's young talent such as teenage Scotland squad member Andrew Robertson and Scotland Under-21 captain Stuart Armstrong on Friday night, although Ryan Gauld and John Souttar could miss out through injury.
"Six of the starting 11 last week have all come through the system," Butcher said.
"The average age of the team last Saturday was 24, which was the third youngest in the Premiership. We are just behind Dundee United and, of course, Hearts.
"It shows what a good blend we have got and a very bright future for the club. We are talking contracts with some of these boys to try and keep them here, because we feel they are very much part of our future."
Butcher, whose side have taken four points from two games since their William Hill Scottish Cup exit, added: "It's exciting.
"It's a great game to look forward to and should be a classic football match because both teams like to get it down and pass it.
"We know if we allow Dundee United to play and get on the ball and pass and move as they can, they are well capable of cutting us open.
"Having said that, we played well against them in early January up at Tannadice, and but for the last 10 minutes we would have won the game. Two-all looks a decent result but we were 2-0 up with 10 minutes left."
Stanton was rewarded for scoring two goals in his first four starts for Hibs by being called into the Scotland Under-21 squad along with Handling this week.
"His form has been fantastic and has been scoring goals and making goals," Butcher said. "He is still a young boy but he is maturing all the time. He is hungry to learn more and be better.
"He excites you. The impact he has had in the Premiership is immense. He brings people to the edge of their seats.
"He scores quality goals. He nearly scored against Celtic with a fantastic shot as well.
"People go away from the game talking about Sam Stanton's contribution. he has taken the game by the scruff of the neck.
"He takes the ball in difficult situations, when he is heavily marked, goes past people, can pass it well, gets in the box, gets shots away, and scores goals. That excites people.
"He has earned the right to be in the squad with his performances."