The National League has asked the Football Association to close the rest of the non-league season.
All divisions are currently suspended because of the coronavirus outbreak.
And a video conference call on Tuesday saw the National League board urged to end the season “as soon as possible for the purposes of player contracts”.
However, Barrow manager Ian Evatt believes if no further games are possible, then the current league positions should be allowed to stand.
"If you were to play a 90-minute football match and something was to happen in the last 15 minutes of a game, the result would stand if it was abandoned. So why is it not the same for a full season?" he said.
Evatt's side are four points clear at the top of the National League table and on course to return to the English Football League for the first time since the 1970s.
The Football Association said on Tuesday that no official decision has been made regarding the end of the 2019-20 campaign.
But in a statement issued to all member clubs and released by fifth-placed Boreham Wood, National League chief executive Michael Tattersall said: “The broad consensus was that our clubs wish for a decision to be made to close the season as soon as possible.
“The FA have been asked to assist us with making the decisions to officially postpone all remaining National League fixtures and to end the season as soon as possible for the purposes of player contracts.
“The National League is also working with the FA to define all reasonable and practical options for the determination of the 2019-20 season, and to provide guidance to clubs on dealing with player contracts, player registrations and the application of the Coronavirus Job Retention Scheme.”
Evatt, however, said that cancelling the season would be unfair and could put his club's future in jeopardy.
"Now if this was halfway through the season or under, you can completely understand voiding a season. But we're talking about, from some clubs' perspective, seven games. Seven games away from completing the season.
"You cannot, you cannot, null and void it," he said.
"We've been top for five months and no-one, no disrespect to anyone, has really come that close to us.
"From our perspective, the interest of fairness would be for us to be promoted and that is my view regardless of where I am right now because of how many games have been played and where we're at in the season."
But Dagenham managing director Steve Thompson said the cancellation of the National League season would help clubs survive.
"What this measure does is help clubs preserve and consolidate their own clubs to ensure everybody can get through this," he said.
"That is why clubs wanted the season to end so they can start looking at how they can make certain they are more resilient for the new season when it starts."