The Nordic nation have already defied expectations by qualifying for Euro 2016, and now they are looking to cause an upset at the finals by making the most of many of the same characteristics that the Foxes boasted this season.
Drawn in a tough qualifying group that featured the likes of the Czech Republic, Turkey and the Netherlands, they finished second to progress to the big event in France and they aren't looking to stop there.
"There is a lot of excitement in the country," Sigurdsson told the Times of India. "The entire nation will be watching. If we play the way we did against Holland, we have a chance to beat everyone this time."
Camaraderie is the secret sauce
Asked what the secret to the team's success has been, and Sigurdsson was straight to the point: "The secret of our game is how we are.
"We all get along well, work hard for each other and are all good friends," he explained, with their "experience of the Premier League" obviously a big "help" too.
However, "overall," Sigurdsson puts it mainly down to the "camaraderie" in the camp.
This is the recipe that gave Leicester success this season, and so the Swansea City man understands the comparisons: "We also play a 4-4-2 formation and are compact defensively like them."
The playmaker described Leicester's title success as "amazing," but believes that Iceland reaching the Euros is "something close to it." Moreover, he stressed that the team are "not done yet" and that "everything is possible" heading into the tournament.
"The lads have been working really hard, the coaches have got ideas. We are ready."
Chance to spring a surprise
Not many people will look at Sigurdsson and co. as a threat this summer, and that should play into their hands. The midfielder said it himself that the team "are under no pressure at all," and so they will be looking to make the most of the opportunity to surprise people.
With the potential of three teams qualifying from the group too, there's an even bigger chance of Iceland getting to the knockout round - which is what Sigurdsson says they are aiming for.
He believes they have the quality to get there too, saying: "Defensively we are good and we have players who can score goals."
One of the latter is certainly Sigurdsson himself, who scored 11 goals for Swansea this season, and he is hoping for that electric form to "come good again in the next couple of weeks.
"I am feeling good about my shape and feel I am in fine fettle heading into the most important tournament of our lives," he said.
However, though he may be Iceland's poster boy, the 26-year-old doesn't think that this adds any pressure onto his shoulders: "The limelight might be on me, but I am as good as my team."
Again, he referred to Leicester and their success story, saying that Iceland as a whole "will look to do well as a unit," just as Claudio Ranieri's team "worked wonders together."
Pressure on the rest
The Nordic nation face Fernando Santos' side in their opening fixture on Tuesday, and Sigurdsson is relishing the chance to share a pitch with the Real Madrid star.
"It will be great playing alongside Ronaldo," he said, however he doesn't envy the pressure that will be on him as his team's star man and one of the best players in the world, never mind at the tournament.
Instead, he is excited to upset the group favourites, as "no one expects [Iceland] to get anything from that game.
"There is a lot riding on them and Ronaldo in particular, but for us also it's a huge game. We need to focus on ourselves and think of getting something from the fixture."