The Bluebirds boss is well aware of stories linking him with Chesterfield.
Evatt took caretaker charge last season but it came too late to save the club from being relegated.
Barrow beat Salford City on Saturday in the live BT Sport game and his team sit top of the form guide.
But he told the club’s official website that he has no plans to walk out.
“I’m obviously aware that the position is open, but that doesn’t mean I’m going anywhere!” he said. “I’m Barrow’s manager, I’ve got a project here and I work ever so hard on the training pitch with the players everyday.
"I think we’ve got that bond and trust now that really pushes us on and moves the club forward, and I’ve got an excellent feeling about it.
“All I can do now is do my own thing, to manage the club the best way I see fit and I think we’re seeing the results of that now. We’re a different team to the Barrow teams of recent times, we just want to make everyone proud.
“Managers who do well are always linked with jobs, but I’m only just getting started here.
“We’ve had ups and downs, we’ve had inconsistencies but I think things are starting to click now.”