The National League said it was looking at "how best to conclude" the season.
But it is not yet known if the competition, which is made up of the National League, National League North and National League South, will also be cancelled with all results expunged.
"The National League is currently obtaining specialist legal advice, is consulting regularly with the Football Association and other stakeholders, and is committed to involving its member clubs in a pending decision on how best to conclude the 2019-20 season," a statement said.
More than 100 clubs have sent an open letter to the FA, calling for it to "urgently" reconsider the decision to expunge seasons from the men's seventh tier and the women's third tier downwards.
The decision is yet to be ratified by the FA Council.
Barrow are four points clear at the top of the National League, with fifth-tier clubs having between seven and 10 league fixtures remaining to complete the season.