A deal for the Premier League to support lower-league clubs during the coronavirus pandemic "could be reached this coming week".
Plans for some fans to return to stadiums from 1 October will not go ahead because of the rising number of coronavirus cases, and it is feared the postponement could have a "devastating" impact on clubs.
Culture Secretary Oliver Dowden told the Andrew Marr Show that England's top flight needs to "start looking after the football family as a whole".
He added that he was hopeful an agreement could be made over the coming days.
"I've been in touch with the Premier League a lot over the past few days. They are working closely with the EFL (English Football League) to see how they can support them," said Dowden.
"The prime minister and I have been clear: the Premier League needs to start looking after the football family as a whole, and indeed they are having productive conversations.
"I am hopeful that they will reach a deal this coming week in relation to that, and then beyond that, look across at all sports."
The fan pilot programme, which had already been restricted to 1,000 people per game in September, has been paused. Dowden said there had been no positive cases from pilots that had already taken place but, under advice from the chief scientific adviser and the chief medical officer, "it would not be wise to undertake any further easements".
"It's not just in the stadium, it's the journey to and from the stadium as well. At each of those points there are chances for further social interaction and risk of virus spreads, so right now is not the time to do it," he added.
Dowden added that the Premier League "appreciates" its help is needed to support EFL clubs and that he is confident an agreement will soon be reached.
In response, Huddersfield Town chief executive Mark Devlin posted on social media: "But Mr Dowden, irrespective of Premier League support, you need to let us start welcoming back fans and business partners into a safe stadia environment.
"So much work had been done on making our stadia as Covid safe as possible, you now need to let us all get on with it."
It is not yet known when fans will be able to return, with existing government restrictions likely to remain in place for six months.
But Dowden said the government was working with clubs and medical advisers to seek "further innovations" to decrease risks.
"We are continuing to explore what would be the ideal solution in the absence of a vaccine, which would be if you have large amount of in-day testing to give people a so-called freedom pass to be able to go into those stadiums," he said.
"We are exploring that. We are exploring further technological innovations. But we are also looking at how we can support the clubs through this difficult period."
BBC Sport's Simon Stone
The BBC was told earlier this month the EFL expected to be given details by the Premier League about what financial assistance it might offer by the end of September.
While the Premier League will continue advancing solidarity payments earlier than normal, BBC Sport understands that, while accepting the need for speed and to be flexible in its approach, it is not completely clear what the EFL is asking for beyond a £250m 'bailout'.
BBC Sport has been told the Premier League needs detailed analysis of what money is needed, for whom and precisely why. Without this, the organisation is reluctant to hand over a cheque at a time when its clubs are feeling huge financial pressure given they are losing the most in terms of fans being absent from stadiums.
Respected football finance blogger Swiss Ramble posted on Thursday that the combined losses of Premier League clubs through the absence of matchday income would be at least £830m if no fans were allowed into stadiums for the remainder of the 2020-21 season.
That figure is regarded as a minimum as it does not take into account sums paid by fans buying merchandise on a matchday because that is calculated in a different revenue stream.