It has functioned on a small budget, and a report commissioned by principal backer Sport New Zealand in 2019 found the status quo was not an option.
Sport NZ stopped providing its annual $100,000 grant from the end of last year and the city council stepped in with a $50,000 lifeline to keep the hall open in Dunedin until July 2021.
A report for city councillors outlines challenges longer term.
The council's total support is already at about $77,000 a year, including a subsidised rental.
A basic refreshing of the hall's permanent exhibition could cost about $650,000.
If the city council were to run the facility, a rates subsidy of $628,000 could be required, the report says.
That would include a marketing budget of $60,000 and employment of a manager, curator, administrator and visitor hosts.
One option is for the council to simply boost its operational grant to about $427,000.
However, this would leave the sports hall still needing to find money from other sources.
The council could persist with the status quo, but that would almost certainly result in the hall's closure.
It could also actively encourage investigation of the possibility of moving the hall to Forsyth Barr Stadium.
The council considered locating the hall's exhibits within the Toitu Otago Settlers' Museum, but this would involve a dramatic cut in exhibition space.
Councillors have been provided with the report commissioned by Sport NZ, by Manuireva Consulting, which found it was not essential for the hall to stay in Dunedin, the status quo was not sustainable and operating as a stand-alone facility at a different site was not feasible.
The consultancy found closing the site at the railway station would be a constructive step towards developing a more sustainable and engaging hall of fame.
A follow-up report is due at the end of March, and city councillors may choose to wait to see what it says.
New Zealand Sports Hall of Fame chairman Stuart McLauchlan said he was pleased dialogue was taking place and he was not giving up on Dunedin continuing to host the hall.
"We want to keep it in Dunedin," he said.
"We're fighting tooth and nail for that."
A factor that could make further intervention difficult for the council is that councillors are already considering a large rates rise. Council debt is also set to soar in the next 10 years.
Cr Sophie Barker, who led the push to give the sports hall a lifeline, leaned towards waiting for more information before committing significantly more money.
She also noted the results were not yet in from a council-backed trial of train trips.
"We have to think about what will be the best mix of products for Dunedin."
