Bradford City say they have been informed of an "ever-growing possibility" that fans will not be able to attend games until 2021.
The League Two club, who on Friday suspended season-ticket sales for 2020-21, said it is "highly likely" next season will start behind closed doors.
The move to stop selling tickets follows a meeting held between the English Football League and its clubs.
The Bantams are currently ninth in the table, four points off the play-offs.
In a leaked recording heard by the BBC on Thursday, Bristol Rovers' Professional Footballers' Association delegate Alex Rodman claimed "we'll be looking at January 2021 [for fans] unless a cure pops up".
Rodman, who was talking to team-mates after a call with clubs, the EFL and PFA, also said the prospect of a 23-team Premier League for next season had been discussed.
BBC Sport understands no final decisions were made during Wednesday's call between club, EFL and PFA representatives, with several different ideas discussed.
The EFL will follow the government's guidelines before making any decisions on whether or not the 2019-20 season can resume, how the issues of promotion and relegation will be decided if not, and when fans can attend matches.
Meanwhile, the Academy Games Programme season - for under-nine to under-18 teams - has been terminated with immediate effect.
The EFL says the decision is "independent of any discussions regarding the resumption of the campaign for first team football," while it has not yet been decided how the final standings will be determined.