Conference North champions Barrow can be a surprise package in the National League this term, says chairman Paul Casson.
The Bluebirds were moved to full-time playing staff status this summer.
Ex-Carlisle striker Lewis Guy and former Walsall forward Ashley Grimes are two of their new signings.
"There are five or six big teams up there, three or four have potential and I'd put us in that category," Casson told BBC Radio Cumbria.
"The bookies have us eighth favourites I think and I wouldn't be terribly unhappy. However, I wouldn't be terribly surprised if we did better than that."
Barrow's last National League campaign ended in relegation, albeit on the back of FA Trophy success at Wembley in 2010 and consecutive FA Cup runs to the third round.
However, two seasons have passed since and manager Darren Edmondson takes his squad into new territory following last's season's promotion.
"I hear it's a big step up, but we don't know because last year we didn't play anyone from this division," Casson added. "Last year I thought we would win but this year we have no idea.
"There's an excitement that comes from that, I think we'll do quite well but I just don't know."