Speaking as a guest on Monday Sport, the U's wing-back said he is hoping that the club will be able to sell out their ticket allocation.
"It would be nice to reach 20,000 and play in front of a big crowd.
"When you play in front of four or five thousand at the Abbey stadium the atmosphere is brilliant so it will be phenomenal."
Gleeson, who is a childhood U's fan, admitted he would become more tense in the build up to the match but he said he intends to enjoy the day.
"As the week goes on we'll start to get more and more nervous, it's every lads dream to play at Wembley."