The Football Association says no official decision has been made regarding the end of the season in England's non-league football pyramid.
The FA held a web seminar with various leagues on Tuesday to discuss the impact of the coronavirus outbreak, with all divisions currently suspended.
Leagues in the seventh and eighth tiers say they all want "to terminate the season immediately".
The FA said it would "make a further announcement at the appropriate time".
"We remain in regular dialogue and consultation with all stakeholders regarding next steps across both the men's and women's National League pyramid and grassroots football," said an FA spokesperson.
"No official decision has been made yet. Our primary concern is for the safety and welfare of clubs, players, staff and supporters during this unprecedented time."
The Essex Senior League - the ninth tier of English football - posted a statement on Twitter on Tuesday stating it had been confirmed that the 2019-20 season would end immediately.
However, much of that statement has since been deleted.
The Isthmian League, Southern League and Northern Premier League - the entirety of the seventh and eighth tiers - have said they are "unanimous in wanting to terminate the season immediately" and have "commenced the process".
"This has to be ratified by the FA Council, so there may be a short delay as the relevant documentation is submitted, distributed and approved," said Nick Robinson, chairman of the Isthmian League.
They say the issue could be complicated, however, as it "may not be possible" for one solution to be applied throughout the pyramid.
If seasons are shut down, it is not clear whether they will be declared null and void or how promotion and relegation issues will be sorted.
There are 14 leagues in the ninth tier, with 20 divisions in the tier below.
Those leagues cover regions all over England, and include the North West Counties League, Hellenic League and the Combined Counties League.