Brighton and Hove Albion chief executive Paul Barber said if the season were to be "frozen" it would be unjust on Liverpool, who are on the brink of their first top-flight title for 30 years
Premier League clubs will attempt to hammer out a plan to complete their suspended season when they meet via a conference call on Thursday.
English football is in lockdown as part of the worldwide bid to slow the spread of the coronavirus.
Top-flight fixtures have been suspended until April 4 at the earliest and while it seems certain that the lay-off will be extended, the postponement of the Euro 2020 finals has created room for manoeuvre.
It is understood the focus at the meeting will be on concluding the 2019/20 campaign at some point rather than on what might happen should they be unable to restart.
There are signs that clubs are split on the way forward.
Brighton and Hove Albion chief executive Paul Barber said if the season were to be "frozen" it would be unjust on Liverpool, who are on the brink of their first top-flight title for 30 years.
But West Ham vice-chairman Karren Brady said if the fixtures could not be completed, the only fair solution would be to declare the season "null and void".
Some clubs lower down the English football pyramid fear they could be forced out of business if football does not return until after the summer.
The English Football League (EFL) has already announced a £50 million ($58 million) short-term relief package to help out struggling lower league clubs.
Underlining the parlous state of some clubs, Scottish Premiership side Hearts announced that it had asked staff to take a 50 percent pay cut.
In a statement on the club's official website, Hearts owner Anne Budge said: "In order to try to prevent a staff redundancy programme and to protect as many jobs as possible, I am proposing to implement a club-wide salary reduction programme.
"We have asked all full-time employees, managers, coaches, players and player back-room staff, with effect from the beginning of April, to accept a 50 percent cut in their monthly salary."
She said she did not know how long the measure would be in place for.