The Bluebirds play their first-ever top flight match against West Ham United at Upton Park on August 17 and Icelandic midfielder Gunnarsson, who was a key contributor in their Championship title last season, is determined to bounce back from a shoulder injury in time for the significant fixture.
"It is improving, but there is a long way to go," he told 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."