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 about his side.
"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 to Raith, 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."
Dundee United manager Jackie McNamara has challenged his side to aim for runners-up spot in the Scottish Premiership.
United sit fifth in the table but McNamara still has not given up hope of finishing second despite Aberdeen's 10-point advantage.
McNamara said: "There's still a lot to play for. I'm sure there will be a few twists and turns between now and the end of the season.
"All we can do is look after ourselves and try and reach the standards we know what we're capable of.
"There are a lot of games ahead so if we do our job and keep getting the results then second place is still not beyond us."
United have been doing their bit in recent weeks with a 3-1 victory over Motherwell last Friday night securing their third consecutive win.
McNamara knows Hibs will be a tough nut to crack under Terry Butcher.
"Terry's teams are always hard to play against," he said. "We found that out when he was at Inverness. They are well-organised and well-drilled.
"However, we will focus on what we are good at. We will try and pass the ball around and make things happen. That's what we're good at and will continue to try and play like that."
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