Kim Streets, chief executive of Sheffield Museums Trust, spoke out ahead of the reopening of the Graves Art Gallery, which occupies the top floor of the Grade II-listed building on Surrey Street.
The gallery will reopen on September 3 after 18 months of closure and following a £455,000 revamp.
But work on the main building has yet to start despite it being listed in 2003 after Hallamshire Historic Buildings stepped in to stave off the threat of demolition.
It estimated the repair bill then at £10m. Today it is three times that.
Ms Streets said: “The gallery still needs quite significant investment. We need investment in the structure of the building, we need council support. We hope this is a stepping stone to arriving at a plan.”
The Graves has undergone six months of work to redecorate and re-clad walls largely untouched since it opened in 1934. A third of the artwork will be fresh out of storage.
The project, which forms the gallery’s first major redisplay in 10 years, was made possible with £455,000 from the Ampersand Foundation.
Ms Streets added: “There is an opportunity with this project to demonstrate what we have and what we can be.”
In 2017 it looked as if the gallery - and the entire library - could move out to make way for a five-star hotel as part of a £1 billion, six-decade agreement with Chinese investment partner Sichuan Guodong Group.
When that failed, the city council, which owns the building, outlined an ambition to turn it into a 'cultural hub', moving the library service into new premises costing £20 million in the Heart of the City II scheme.
That has not happened and in recent years a lack of investment has started to show.
In November 2019 the Graves Gallery had to close for several days when a problem with the heating meant the temperature was too cold for visitors. Bosses said it was due to the age of the heating system in the Central Library building.
A statement said: ‘It no longer heats much of the Graves Gallery. As tenants, we continue to work with Sheffield City Council, who own the building, to explore long term solutions for the problem, but unfortunately the repairs require significant investment.’
In January last year it was forced to shut early because of a problem with the lighting on the building's main staircase.
Regular visitors grew used to drips from the ceiling in the cafe on rainy days.
The Library - and the Graves - did not reopen when Covid restrictions were eased in 2020. Later that year it was earmarked for a £9m scheme to fix a backlog of repairs - a month after Ms Streets warned ‘time was running out’ for the historic building.
The Graves Gallery will be open from 10am-4pm, Monday-Saturday from Friday September 3. Entry is free and there is no need to book but Covid safety measures will be in place.