The 24-year-old, who has already racked up 51 international appearances for his country, scoring 17 times in the process, says that both he and his team-mates are in fine fettle at the moment and feeling confident of springing a major surprise in France this summer.
“I’m feeling good ahead of the tournament. I think we [Switzerland] can go further than a lot of people think.” Shaqiri told Goal.
“Two small teams have won before, Greece in 2004 and Denmark before that. I’m not saying we’ll win, but I don’t think we should be written off.”
Indeed, Shaqiri is confident that his side will make the last 16, despite having to face some tough opposition in group stage.
Romania and Albania join Switzerland in Group A alongside tournament hosts France, whom the Stoke City man recognises as being the clear frontrunners to top the pool.
“It’s a tough group with France, who are, of course, favourites, but I think we’ll get out of the group and hopefully the momentum will take us on further.”
Shaqiri made his international debut in 2010, aged 18, and after helping his nation reach the quarter-finals of World Cup 2014, he played a key role in Switzerland finishing second in their Euro 2016 qualifying group, behind England, where he is now playing his domestic football.
He arrived at The Britannia Stadium from Inter in August 2015 for a club record fee of £12 million (€15.4m) and is hoping to be better attuned to the English game next season, after a gruelling debut campaign in the Premier League.
“I’ve enjoyed English football and it’s prepared me well for this summer," he explained. "But I think I’ll have adjusted better to the League by next season.
"However, for now, I’m focused on performing for my country. We have some good players and if we all do what we are able to, we will do well.”
Shaqiri's Switzerland side face Albania in their opening Euro 2016 game in Lens on Saturday at 1500CET.