The Iceland international has focused his attention on returning from a dislocated shoulder in time for Cardiff City's Premier League opening fixture away to West Ham
Having played a significant role in helping the Bluebirds win the Championship title, scoring eight goals in 45 appearances last term, the midfielder is determined not to miss the side's historic fixture against the Hammers.
That gives 24-year-old Gunnarsson just over four weeks to prove his fitness following the injury setback he suffered at the start of June while away on international duty with Iceland.
"It is improving, but there is a long way to go," he informed the club's official website.
"I am working hard on making my shoulder stronger and more stable, but it's not quite time for contact training yet.
"That being said, right now I am on schedule.
"It happened when I fell awkwardly and the shoulder dislocated. It's just one of those things. I came back early for treatment and my aim is to be ready the West Ham match."
Malky Mackay's men will embark on the club's first season in the English top flight since 1961-62, and Gunnarsson is licking his lips at the prospect.
He added: "I can't wait to be judged as a Premier League player.
"It's going to be an exciting challenge. We won’t fear it. We are all excited to be part of what is the most watched league in the world.
"I feel proud when I think of how Cardiff City achieved promotion, winning the title by a good margin. We can't wait to be part of the biggest league in the world."