Football needs to look after itself to survive amid the coronavirus crisis, according to sports minister Nigel Huddleston.
The government is not expected to bail out clubs who are struggling during the pandemic.
The Premier League and Sky Bet Championship returned behind-closed-doors last month with Leagues One and Two ending their regular seasons and only holding the play-offs given the lack of income from gate receipts.
EFL chairman Rick Parry has warned lower league clubs are facing a £200million financial black hole by the end of September.
The Premier League advanced their £125million solidarity payment in April but there has been no approach from the EFL for more money and Huddleston believes the leagues need to look after each other.
He said: "We're in conversations with them, but, to be honest, I think EFL, Premier League and the FA all understand that they've got a responsibility to each other and to make sure the whole pyramid survives. I expect everybody to play their part.
"There's a responsibility for the football pyramid to look very carefully at the dynamics and the financial flows.
"There's a lot of money in British football and we need to make sure that it first and foremost looks after itself.
"Given that there's a lot of money in British football, taxpayers would not necessarily expect that that's the sport that they're going to have to delve into their pockets and bail out.
"We are having conversations with all the key players. Premier League have advanced £125million so far and if more's needed, then we'll have those conversations.
"To be fair, they are having conversations amongst themselves, and also then looking at slightly longer term.
"We've announced a grass-roots fan-based review of football governance. I don't think that can be divorced from the financial aspects as well.
"We'll see how things go in the long term, but there are some clubs that are really going to suffer, so we really need to make sure that we can open up as fast as possible but also safely."
The government is planning to allow fans into Premier League games and other sporting events from October 1.
The PA news agency understands top flight clubs have discussed having supporters at pre-season friendlies.
Pilot events with fans at cricket, horse racing and snooker are happening this week and Huddleston remains confident plans for October are on track.
He said: "The October 1 deadline is certainly the target that we're looking at.
"In the past, if you look at various announcements we've made, some have been put forward, some have been pushed back, but I think that's a pretty firm one because we've got plans for not only the immediate pilots, but the next series of pilots.
"We genuinely want to make sure that we learn the lessons from those pilots. We're really just talking just over two months away.
"In the whole scheme of things, it's not that far away – 60 something days, and we'll be there. So I would be surprised at this moment in time is that date moved. But I'm confident we'll meet that date."
Fans have started to return to stadiums this week for the first time since the pandemic shut down sport in March.
A thousand supporters attended Surrey's friendly against Middlesex at the Kia Oval on Sunday. Edgbaston in Birmingham is also hosting a two-day friendly between Warwickshire and Worcestershire.
The World Snooker Championship, which starts on Friday, will become the first indoor event to pilot the safe return of fans, and 5,000 members of the Goodwood Horseracing Club will attend the Festival on Saturday.
"So far it looks like it (the cricket) has gone pretty much as predicted," added Huddleston.
"There were measures expected and fans behaving themselves. There's quite a lot of pressures on these, we need and want them to go well. We have to make sure they are proper learning experiences as well.
"We are looking at them as a learning opportunity so we're not expecting them to be perfect and genuinely looking at them for what needs to change and needs to be improved. They are really important."
