The council could put in a formal request to take over running the hall, but doing so could cost hundreds of thousands of dollars and it has no budget for that.
The hall of fame doubles as a sports museum housing memorabilia such as gold medals won by Sir Peter Snell and it has been located at the Dunedin Railway Station since 1999.
It has existed on funding provided by Sport New Zealand and the council, which also provides the space, but the status quo is considered unsustainable.
A $50,000 lifeline provided by the council to keep the hall open expires next month.
Dunedin City Council staff reports say $650,000 would be needed to redevelop the exhibition and about $628,000 a year would be required for operational costs from 2022-23.
Cheaper options include allowing the hall to either move or close, and providing interim support in 2021-22 until a decision is made about the hall’s final location.
The council has little room to move if it steps in with more funding or it risks breaching a self-imposed cap of a 10% rates increase, unless it cuts other proposed projects.
Councillors will consider their options next week.
The New Zealand Sports Hall of Fame Project Steering Group would make the final decision on the hall’s future and a consultancy reporting back to it would call for expressions of interest for hosting the hall, a council staff report said.
Doubts have been raised about the suitability of the railway station to continue to host the sports museum.
However, a survey of 63 visitors in March showed 55 of them discovered the hall of fame as part of a visit to the station.
Minister for Sport and Recreation Grant Robertson said the hall was a great place and it was a credit to chief executive Dr Ron Palenski and everyone who had supported it.
Asked about calls for a Government funding boost, Mr Robertson said the sports sector had an opportunity to step up.
"Sport NZ has at times worked with Ron and we will continue to do what we can, but I think this is an opportunity for the wider sports sector and people who believe in the Sports Hall of Fame to step forward, too."
A national sports museum is proposed to be built in Christchurch and its backers are in talks with the University of Canterbury about potentially hosting an international sports research institute incorporating digital sport archives and a national sports library.
National Sports Museum Trust of New Zealand foundation president Bruce Ullrich said the trust had not been actively pursuing the hall of fame, but it would be happy to incorporate the hall into its initial planning.
The trust was looking into making its museum a legacy project to celebrate the 10,000 New Zealanders who were involved in the 1974 Commonwealth Games at Christchurch, Mr Ullrich said.
The 50-year anniversary for the Games is in 2024.
