The club hope to be in a position to agree terms their new boss over the next few days.
The Bluebirds have been searching for Ady Pennock’s replacement for three weeks.
The Kent-based manager left having kept the club in the National League on the final day of last season.
Barrow are the only club in the National League without a manager following Dagenham’s decision to appoint Peter Taylor and Terry Harris in midweek.
Although the club may not make an announcement before the early part of next week, a deal is expected to be signed over the next few days.
Managing director Andrew Casson told the Barrow News and Mail that there has been movement with their hunt nearing a conclusion.
“We're finalising secondary discussions in advance of having a discussion as a group on Friday and into the weekend about who we think is best and ultimately making the final decision,” he told them newspaper.
“There is a gap between decision and announcement, just given the negotiations regarding the contract and everything like that.
“But I'd like to think we would have a decision on Friday or Saturday, with an announcement made early to mid-next week – assuming there is an easy agreement once we have picked the man for the job.”