Arsenal's under-18s are in the quarter-finals of the tournament where they face CSKA Moscow at the Emirates Stadium on Monday after beating Inter Milan in the previous round.
Diaby is jealous of the club's youngsters and wishes he had the chance to play in such a tournament when he was younger.
"I would definitely have liked to play in the NextGen Series," he told Arsenal.com.
"When i was younger we always used to talk about this kind of competition, to play all over Europe against big teams.
"That was a real dream but unfortunately at that time it didn't happen. But I think it is really good for the youth players, it is great experience for them. At a young age they can feel the atmosphere of playing in the European Cup, so that will really help them."
The Frenchman believes Arsenal's youngsters have what it takes to go all the way in the competition, having played alongside a number of the club's most promising youngsters.
"There are some very good players in there, people like Serge Gnabry and Chuba Akpom," he said. "They train with us sometimes, and I have played with some of them in the reserves. Serge came away with us to Germany in pre-season and was really impressive.
"I think we have a bright future and I wish them good luck against Moscow."
Should Arsenal progress they would face Chelsea in the semi-final, with Aston Villa vs Sporting Clube de Portugal the other last four fixture.