The under 18s claimed one of their best results in years by coming from behind to win 3-1 at Swansea City on Tuesday night.
It sent them through to the last 32 and a meeting against another Premier League club.
United’s youngsters play their home games at Didcot Town’s Draycott Engineering Loop Meadow Stadium.
But Allen, the club’s youth team manager, feels it would be a fitting reward to have the game at the Kassam, just like they played Bolton Wanderers two seasons ago.
He said: “It’s at home so it is provisionally at Didcot, but hopefully we’re going to try and have it at the stadium if possible.
“Hopefully the powers that be will let us do that, because it’s not very often you get these occasions.”
The cup run has not gone unnoticed with the senior players and several tweeted their congratulations within minutes of the final whistle in Llanelli.
Allen said: “It’s great and shows togetherness of the club because the first team boys are really interested in how the youth team guys get on.
“We train at the same facilities so everyone is together and it goes to show that when straight after the game we’re getting tweets from the senior lads saying well done. It’s brilliant.”