The unusual pyramid-shaped building has been the entrance to the Southland Museum and Art Gallery at the edge of Queens Park since the 1990s.
It was closed in 2018 because it is earthquake prone.
An independent governance group set up by the Invercargill City Council last year to "reimagine" the museum and art gallery has produced a report, to be considered by councillors on Tuesday, presenting options for reinstating the facilities.
Its favoured option is to demolish the pyramid and build a new 4,150sqm building within the same footprint.
The group, Runaka appointee Evelyn Cook, Gavin Bishop, Trish Lindsay, Lou Sanson, Roger Beattie and Simon Owen, suggests a new permanent stand-alone storage facility should also be constructed.
The total project would cost $75.6 million.
Other options include earthquake strengthening the museum building to standard , fully refurbishing the pyramid building, and demolishing the pyramid and building a smaller museum with a storage facility.
The costs of those options range from $57.1 million to $65.2 million.
Council leisure and recreation group manager Steve Gibling said in the report the option of the smaller building provided the best overall outcome for the project, when
balancing the "vision and critical success factors", the community experience as well as the risks and financial costs.
He noted a decision to demolish the pyramid could spark a lot of feedback from the community.
"Taking into account the community’s response to the closure of the pyramid building in 2018, [demolition] is likely to receive a high level of response from the community."
The group recommended the museum’s tuataras get a new, separate enclosure in Queens Park.
All of the options were expected to be delivered by mid-2027.
Detailed information would be made available to the public and feedback sought during public consultation from March 24.
