Barrow could be voted back into the English Football League if the season is not finished, 48 years after they were removed, says director Levi Gill.
Barrow are four points clear at the top of the National League and pursuing a return to the EFL, having failed to win re-election to Division Four in 1972.
But the National League has asked the Football Association to close the rest of the campaign because of coronavirus.
"We would first need to be recognised as champions," Gill told BBC Sport.
He says that decision will fall to the National League and could be decided either by taking the current standings or deciding them on a points-per-game basis, if their remaining nine fixtures cannot be completed.
League One side Bury were expelled from the EFL earlier this season, meaning there is currently a vacant spot in the structure - something that could favour Barrow's bid for promotion.
"If the National League recognises us as the champions of the division then I would say the normal process would kick in, and it's up to the EFL to accept us," added Gill, who says the Cumbrian outfit have already proved they can comply with EFL regulations.
"In principle, we have been accepted - they have looked at the business, looked at the ground, what we want to do, and that's all been approved."
Bluebirds boss Ian Evatt also says "it will probably end up a vote on whether we go back into the league or not" - but Gill is happy to take a place in League Two however it comes.
"It is a shame for the fans," added Gill, who says the club have been praised by rival supporters for their football this season, and even dubbed 'Barrowcelona'.
"To have got promoted after 48 years on the pitch would have been amazing. It would be nice to do it properly, but to do it at all is amazing."
Barrow lost their Football League place in 1972, despite finishing third bottom of what was then known as Division Four, when the bottom four clubs were required to submit to re-election.
That process continued until 1986 when automatic relegation to the National League - formed in 1979 as the Alliance Premier League, and subsequently the Football Conference - was introduced.
But in 1972, Barrow were voted out, with Hereford United - who had finished second in the Southern League - taking their place.
"Hereford had just knocked Newcastle out of the FA Cup, it was on television, the famous goal from Ronnie Radford, so they were a big deal," explained Gill.
"We had finished third bottom and they hadn't even finished top of their league.
"There's still that sense of injustice at being voted out."