Crystal Palace chairman Steve Parish says that unless Premier League clubs can find a way to stage matches soon, it may be a “very, very extended period” before the top flight returns.
Speaking on BBC One’s Andrew Marr Show, Parish said that initial plans for league matches to be staged again from June may prove unfeasible.
“We would be derelict in our duty if we didn’t find a way to try and bring the game back,” he said.
“It may prove beyond us.”
At least three clubs – Watford, Brighton and Aston Villa – are opposed to the plan to stage matches at neutral venues under ‘Project Restart’, while club doctors have raised concerns over aspects of the proposals.
Parish will be part of a meeting of Premier League club officials on Monday where discussions will continue over how they could get their teams back on the pitch.
In Germany, where the top two divisions are set to restart on 16 May, second-tier side Dinamo Dresden have placed their entire squad and coaching staff into isolation for two weeks after two players tested positive for coronavirus.
A previous wave of 1,724 tests carried out last week by the Bundesliga returned 10 positive results.
“The German example could provide a blueprint for us and clearly we can see some of the early challenges,” added Parish.
“They may prove insurmountable, but the concern for us is that if they prove insurmountable now then we may be in for a very, very extended period of not being able to play and that has huge ramifications for the game.”
Premier League chief executive Richard Masters has previously predicted a loss of "at least £1bn" if the Premier League fails to complete the 2019-20 campaign.
Parish believes that deciding the final league positions on the pitch, rather than relying on points per game or taking the current table as the final outcome, is preferable, even if conditions are far from ideal.
“Deciding it competitively would be best, obviously if we can play in our own stadiums that would be preferable for everybody, but for the moment that situation is with government and the authorities and not with us," he said.
“The police have made it clear that they don’t think they can police every ground.
“I have enormous sympathy with [Watford chief executive ] Scott Duxbury’s position. Having said that, I think it may well prove to be the least worst option.
“There are no easy answers, we have to work through it as a collective and I think we will come out with a consensus in the end.”
Parish also underlined that he and his colleagues are keeping football in perspective during an outbreak in which, as of 11:30 BST on 10 May, at least 31,587 people have died after testing positive for coronavirus in the United Kingdom.
“Football is entirely unimportant in the context of the public health crisis, that has to come first,” he said.
“We will want assurances as clubs that we are not taking resources away from anyone. We simply can’t take tests away from anyone who is more needful than us.
"We have been told so far that these are private facilities that are not being utilised for this particular public health crisis. We will all want more clarity on that, it is essential that that is the case.”