"We want to bring the right parties to the table, including the council," Edgar said.
The Dunedin City Council provided its own $50,000 lifeline to keep the hall open after Sport New Zealand suspended its $100,000 annual grant from the end of last year, but councillors decided in a tight vote this month not to provide another lifeline.
They also decided unanimously not to express interest in continuing to host the hall at a council-owned venue.
It has been at the Dunedin Railway Station since 1999, but this is no longer considered viable and the Sport NZ funding cut upped the ante on securing an alternative site.
The hall of fame is considering expressions of interest from parties that could provide a long-term home outside of Dunedin.
The city council opted out of that process, but Edgar said his family had not given up.
He hoped the council would match his family's $50,000 offer and, if it did, this would keep the hall open in Dunedin for another year.
A viable proposition could be worked on in the meantime.
If the council did not contribute $50,000 extra, Edgar believed the money could be raised anyway.
Hall of fame chairman Stuart McLauchlan said keeping the existing operation open would be helpful.
The hall held many items on the condition they were on display.
McLauchlan called the Edgar family's offer to boost the existing operation generous.
Dunedin Mayor Aaron Hawkins said he expected the move to be welcomed.
"I'm sure that will strengthen their case with the other funders or sponsors they're putting applications in front of," he said.
The council could consider future funding through its annual plan process early next year, Hawkins said.
Sport NZ was open to "entering into discussions around investing in a revised model, once there is a clearer picture of what that future model might look like", a spokeswoman for the agency said.
One problem for the Dunedin indoor sports complex the Edgar Centre, touted as a possible home, is it would need to expand to accommodate the hall of fame and the vast majority of the capital expenditure needed has yet to be sourced.
Graphics entrepreneur Sir Ian Taylor said he expected national funding for an interactive national facility could be obtained.
Sir Ian walked back on a statement he made earlier about the mayor being happy to spend $40,000 on painting dots in George St, saying he had not realised the NZ Transport Agency contributed a large subsidy.
However, he believed it was not hard to find other examples of dubious council spending and the important thing to remember was Dunedin had a head start on hosting the hall of fame because of Sir Eion's $500,000 pledge and $200,000 more from investment firm Forsyth Barr.
"Let's make sure this city doesn't lose an opportunity to have an attraction of national importance."
