For the first time since 2004, Zwanziger will not be part of the official Germany party for the trip to Poland and Ukraine.
He will step down from his position as German FA (DFB) president in March but will nevertheless be watching the games and hopes to be entertained, even if it does not culminate in Germany lifting the trophy in Kiev.
"Of course we are all dreaming of being able to win a title again after 1996, but nobody can predict if that will happen," Zwanziger said on the DFB's website.
"There are so many nations at a very high level at a European Championships and it usually comes down to minor things or even a bit of luck.
"For me, success would mean playing beautiful football.
"If we then win the title, that would be even better. The chances aren't bad and I have all of my faith in the work of (coach) Joachim Low, (general manager) Oliver Bierhoff and the whole team."
Wolfgang Niersbach will embark on his first official trip as DFB president next summer and Zwanziger is pleased that he, pending an official election in March, will be replacing him at the helm.
"I think Wolfgang Niersbach is the best candidate," Zwanziger added. "I am glad that the decision of who will succeed me has been made so quickly.
"I have been working with him for 20 years and I am convinced that he will lead the association excellently.
"He will receive my full support."