Stoke City's Given, who turned 40 on April 20, could be between the posts at the Stade de France against Sweden.
But the next day in Bordeaux, Hungary's Gabor Kiraly is all but certain to start against Austria, and Kiraly is 19 days older than Given - born on 1 April 1976.
Currently, the oldest player in Euro history is Germany's Lothar Matthaeus, who was 39 years 91 days when he played his final game at EURO 2000.
"Back in '96, I was delighted to play one game for Ireland, so to think I am still here 20 years later is phenomenal," Given said.
"I don't know if it's good or bad when you're the oldest player involved. I never set out to do that. I'm just delighted to be here, to be honest."
While Given has more caps than Kiraly (134 to 103), Kiraly has the edge when it comes to recognition - for his trademark baggy grey jogging pants.
"I'm a goalie, not a top model. It's essentially a question of comfort," Kiraly said.
For Hungary coach Bernd Storck meanwhile, Kiraly's age is a non issue.
"I don't care if a player is young or old, he has to be good. Gabor is good - he's outstanding. He radiates confidence and is a goalkeeper with an incredible aura and charisma. He will help us be successful at EURO 2016," Storck said.