Rochdale chief executive David Bottomley has warned people that a circuit break in the current campaign is “inevitable.”
Eleven clubs in League One have had games suspended as a result of a coronavirus outbreak since December 15, including Sunderland.
Lincoln and AFC Wimbledon also returned positive tests but claim to have been told by the EFL that their game at the weekend had to go ahead.
More and more clubs are reporting positive cases as the weeks go bye and Prime Minister Boris Johnson has plunged the country into a third national lockdown.
Elite sport has been given the green light to continue, but a number of clubs are calling for the season to be extended with a fixture backlog set to disrupt the remainder of the campaign.
Bottomley told BBC Manchester: "Surely just for a month until the vaccine starts to get rolled out, we could have a break.
"[Suspending the league] is inevitable. Hospitals across the UK are being told they are to face a massive surge in Covid cases so who are we in football to be trying to add to that situation?
"My fear, in common with that of a number of other League One chief executives I spoke to on Friday, is that there will be so many players test positive that we'll almost have to suspend the season.
"Human life is far more important than whether we play football matches, surely.
"I'm talking from personal experience. My 85-year-old mother has tested positive and has been in hospital from the beginning of December with Covid. It's best football takes a break and step back."
