Inverleith House is set to shut as an arts venue after the exhibition it is currently hosting – entitled I Still Believe In Miracles – ends tomorrow.
However, a petition launched this week has already generated 5000 signatures and prompted a senior councillor to intervene.
Many of the supporters will take part in a “mass visit” tomorrow afternoon to show the attraction is much-loved.
Bosses at the Royal Botanic Garden admitted earlier this week that the gallery was proving too costly to run, with plans being drawn up to find another use for the historic building.
But Inverleith councillor Lesley Hinds insisted the notice period ahead of the closure was too short and said she would lodge an emergency motion at the next full council meeting in a bid to win a reprieve for the gallery.
Councillor Hinds said: “The announcement of the closure was made on Tuesday for Sunday – that is a shocking length of notice for a public body to give people for closure.
“My understanding is that there was a report looking into future and alternative uses of the building and that has not been made public, which for an institution funded by public money from Creative Scotland shows a lack of openness.
“Our main aim at the moment is to keep the gallery open past the Sunday closure date and ensure it remains open until at least Thursday when we can air constituents’ views before the full council.”
It has also emerged that Creative Scotland provided £80,000 funding for the gallery in December – cash which was supposed to sustain it for the next five years.
Seonaid Daly, director of Scottish Contemporary Arts Network, also called for “increased clarity over the proposed use of the space”.
She added: “The loss of Inverleith House would be a massive loss to the Scottish art world.
“It’s extremely well loved and well respected and that has been evident in the support for our mass gathering tomorrow.”
The Georgian building has featured works from artists including Douglas Gordon, Jim Lambie, Richard Wright and Louise Bourgeois, among others, in the past and was the birthplace of the Scottish Gallery of Modern Art in 1960.
A spokesperson for the Botanics said: “We will respect any decision the council makes and will be happy to sit down and discuss their objection to the closure with them, but until that time, our position remains that the gallery will close as contemporary arts venue on Sunday until we determine the best possible revenue stream for it.”