The National League season may not start as planned on 3 October if supporters are not able to attend, BBC Sport understands.
Plans for fans to return to watch live sport events in England from 1 October will not go ahead, cabinet office minister Michael Gove has said.
The National League will consult with clubs once the government has outlined the latest measures.
A decision is expected at a board meeting on Thursday.
The league had previously received approval to hold test events with fans.
Last week it was announced that up to 1,000 people were to be allowed to watch friendly matches at Dagenham & Redbridge, Yeovil Town, Dartford and Notts County on 22 and 26 September.
Sports are to be asked by officials for their assessments of the financial impact of playing behind closed doors for several more months, while the government is said to be keen to work with sports on a possible support package that would enable them to survive.
National League chairman Brian Barwick has previously said he feared clubs would "suffer severe economic hardship" if spectators were not allowed to return to stadiums in the near future, with teams at that level more reliant on matchday income.
The 2019-20 National League regular season was brought to an early conclusion because of the coronavirus pandemic, although play-off games in its three divisions were played behind closed doors in July and August.
News 'a bombshell' for clubs
Chesterfield chief executive John Croot has said nobody at the club had any indication that the plan to allow fans back into stadiums in October was going to be scrapped.
"I was astonished. I just saw it on television like millions of other people and hundreds of our supporters," he told BBC Radio Sheffield.
"It was the first I had heard of it and nobody in the club had any idea that bombshell was coming our way."
He added: "We're OK financially for the time being. Speaking to other clubs there are some out there who are weeks away from real issues."