Vicente del Bosque's side will be hoping to retain the title they won four years ago in Kiev, when the Ukraine and Poland jointly hosted the tournament.
"I hope that Spain reaches at least the final and wins. It depends, as always, on the players' physical condition because most of them have come off a long season," Puyol was quted as saying by goal.com on Saturday.
"We have a very good team with good players. The generational change is the law of life, you know? There are several young players with international experience in their clubs.
"(Iker) Casillas, (Gerard) Pique, (Sergio) Ramos, (Sergio) Busquets,(Andres) Iniesta, Cesc (Fabregas), (David) Silva, they all have spent many years, they are leaders. And you also have youngsters like Thiago (Alcantara), Saul (Niguez), Isco."
The 38-year-old, who was one of Spain's key men in their World Cup triumph in 2010 also highly praised former teammate Pique and added that Brazil's Thiago Silva is the world's best defender at the moment.
"Pique is the best at BarÇa and is a very important player. I've been so fortunate to play many years with him," he explained.
"We understood each other very well and I think we matched. Best one right now? I love Thiago Silva (Brazil), a complete player who can read the game. He is fast, has good output of the ball and great passing. I like when people say we are similar."