Brighton chief Paul Barber says Premier League clubs will seek to assist lower league clubs.
Barber is mindful of the damage a lack of revenue will cause clubs in lower divisions.
But he said it was too early to talk about support from the Premier League during the coronavirus shutdown.
Albion's deputy chairman and chief executive said: “We're all suffering at the moment, Premier League clubs as well.
“First of all, we've got to safeguard our jobs for our people. We've got to pay our bills and then, if we can, provide help for clubs further down the football family.
“Obviously it would be a good thing at a very, very difficult time.
“The last thing anyone wants is for any Football League club to go out of existence.
“The football family is just that. It's too early to say how or in what way we could help, but certainly it is something on our minds.
“It is not that long ago this club were in the lower reaches of the Football League so we are certainly not looking down on clubs in difficulty.
“We certainly do have a lot of care but also have to focus at the moment on our own business."