The winger was only eight when he was part of the Halloween crowd squeezed into Celtic Park as Martin O'Neill's side beat Juventus 4-3 only to head out of the tournament at the group stage on nine points.
He was there, too, against Barcelona and Bayern Munich and, a little older, he was also a ballboy at some of the biggest occasions at the stadium. Now he wants to play his part.
As Celtic take on HJK Helslinki tonight on a mission to get through to a play-off for the Champions League, the 19-year-old is desperate for the opportunity to compete on the biggest stage of all.
He watched the first leg at Celtic Park as Neil Lennon's side won 2-1 and he is confident that the Parkhead side have enough about them to progress.
"I would love the chance to play in the Champions League," he said. "I grew up watching Celtic in the competition and I remember coming to games with my family.
"European nights are the ultimate aim for every player because you know that the calibre of player you are up against is excellent. If you want to improve and you want to learn that is the best way to do it."
Lennon, of course, was part of those Celtic sides who helped to restore the club's reputation in Europe.
As a player he was involved in the run to the Uefa Cup final in 2003, but competing at that level as a manager is another challenge.
There will always be critics, especially this season, who will point to the fact that winning the SPL with Celtic does not reflect your worth as a manager, but holding your own in the Champions League will get the attention.
Given that the whole of Scottish football has been hit financially with the Rangers situation, getting into the competition would go a long way to balancing the books at the club this season.
However, it is for different reasons that the competition still holds a pull for players.
"I just think that it is an amazing tournament," said McGeouch. "You watch it on TV and when I was younger I was at mostly all of Celtic's Champions League games and I'm sure most would say that playing there is something that you grow up aiming for.
"It is not easy to get there, though. We know that we need to be at our best.
"But if we can get our heads down and get through then we know that the rewards are absolutely massive."
McGeouch was an unused sub on Saturday as Celtic had a shaky start to the campaign against Aberdeen.
It was far from a vintage performance from Lennon's side who will need to find greater fluency against the Finns tonight.
"I want to play as big a part as I can but I know that I am still young and I still have a lot to learn," he said.
"The manager has already shown that if he thinks you are good enough then he will have no qualms about throwing you in.
"I just have to get my head down and work as hard as I can."