Rugby Football Union chief executive Bill Sweeney says the organisation is looking to phase in cuts to funding for the Championship over two seasons.
Second-tier clubs say they are under threat after plans to slash their funding in the summer.
Currently the RFU pays the clubs about £534,000 per year, but that will drop to a 2015 level of £288,000 per club.
“We’re looking at phasing that reduction over a longer period over two years,” Sweeney told the BBC.
Speaking for the first time about offering a potential compromise, he told Radio 4’s Today: “We have gone to them and said ‘look, we can reschedule these cuts over a period of two years, and work with you in terms of how to how to manage that situation’.
“The other thing we said is ‘let’s sit down and work together as a group and figure out what is the role of the Championship’.
“We haven’t just cut this to save £3m. We’ve cut it because we are not clear of the benefit we’re getting from that spending.”
The cuts announced on 12 February were described as “immoral and irresponsible” by Jersey Reds chairman Mark Morgan, while Bedford Blues chairman Geoff Irvine said the decision was “giving Premiership Rugby all that they want with regard to ring-fencing, in all but name and with none of the financial commitment or support”.
Cornish Pirates, who are third in the Championship and are planning to build a new stadium with the aim of making the Premiership, will stay fully professional.
In response to Sweeney’s interview, Pirates chairman Paul Durkin told BBC Sport that while he welcomed the move to phase in the cuts, many clubs had already made financial commitments for next season before being told about a funding reduction.
“It’s still devaluing the Championship and we need to look and see what we can do with the RFU in the future to ensure the Championship is viable and seen as the second tier of professional rugby in England,” he said.
“I welcome the fact he’s rethinking and looking at what needs to be done. It’s a bit late as this first savage cut came when most clubs had already been involved in negotiating contracts for next season.
“He may have listened to what we said, but it’s still a big issue for most clubs. Whatever that issue is, budgets had been looked at and had been worked on prior to any cuts.
“We as the Championship clubs need to get together to look at this, discuss the implications over the two-year period. We need to see what the options are.”
‘I do personally care very much’
The 12-team Championship was set up in 2009 as a professional second tier, replacing the 16-team National One, and saw its funding rise after England hosted the Rugby World Cup in 2015.
But since the Championship’s inception it has been dominated on many occasions by the side relegated from the Premiership in the previous season. Only Exeter and London Welsh have ever won promotion having not been a Premiership shareholder.
Championship clubs are concerned that the cuts will make it easier for the Premiership to be ring-fenced, meaning there is no prospect of promotion to the top flight, or relegation from it.
But Sweeney says the £3m cut is needed if the RFU is to fund other parts of the game.
He continued: “We have 2,000 clubs out there. There are a lot of things that we want to do around developing the women’s game, facilities and the grassroots game, and that needs funding and we simply can’t fund everything to 100%.
“How do you apportion the money appropriately? And do we feel we’re getting the right correct level of return?
“If you actually look at the spend on the Championship since 2015, our cuts in the professional game have gone down 15%, our cuts in the community game have gone down 5%. If you take out that 100% increase that Championship clubs (have had), it’s gone down by 3%. So actually, they’ve borne less of the pain of the last five years.”
Sweeney has also been accused of being “uncaring” by Nottingham chairman Alistair Bow – an accusation Sweeney denies.
“I can understand how he might feel that way but I can promise that I do personally care very much. We do care very much,” said Sweeney.
“We’ve got 560 people here at the RFU. We’re all very passionate about rugby. I’ve worked in the corporate sector now in the sports sector. And one of the things I can say to you is it’s a privilege to work in the sport that you love.
“But when you make decisions in the sporting world, you’re dealing with people’s emotions, and it’s very difficult.”