The former Odeon on South Clerk Street, a 1930s art deco-style building, is set to be partially demolished and converted into a luxury hotel.
Developer Duddingston House Properties (DHP) intends to preserve the facade and entrance foyer, but says it is not economically viable to renovate the whole building.
Its plans for a 231-bedroom hotel, artists' studios and restaurant have already been approved by the city council but are awaiting listed building consent from Historic Scotland.
Now local people have set up a charity in a last-ditch attempt to preserve the B-listed building. They hope to raise the cash to buy it and run it as a cinema, film library and cafe. They are urging Historic Scotland to oppose the plans and support calls for a public inquiry.
Edinburgh-born Bremner, who is best known for his role as Spud in Trainspotting, has said he is keen to support the group.
He said: "I'm happy to sign the petition and additionally would be happy to be involved with the independent media centre."
Actors Sir Sean Connery, Brian Cox, James Cosmo and Dougray Scott have all campaigned to save the cinema since it closed in 2003. The Cinema Theatre Association, the Theatres Trust and the Southside Association are also backing the campaign.
Campaign organiser John Need said he was confident they could raise the money through grants and local fundraising activities.
He said: "This is a building that has made a significant impact on Edinburgh. It's nonsense to say nothing else can be done with it. DHP are saying they have not had another serious offer, but we think this is an alternative.
"This could turn into an economically viable and vibrant space for the community and a nationally important creative hub for artists and filmmakers."
He said the cinema had been allowed to become derelict.
He added: "Last time we visited, there was rising damp on the walls and the interior was in a terrible state of disrepair. Nothing appears to have been done to repair or clean or maintain the building since 2005."
Edinburgh Central MSP Sarah Boyack said she would support calls for a public inquiry.
She said: "There was a strong local campaign to save the cinema and I have written to Culture Minister Mike Russell making him aware of the situation and urging him to consider the case for the preservation of the cinema."
But a DHP spokesman said that no feasible alternatives had been put forward. He said the developer would be keen to work with the group if it had a workable solution for restoring the building.
He said: "We didn't buy the building to knock down the auditorium. I'd be delighted if someone would make me an offer for it. We've continually said we would consider any credible proposal, but I haven't seen any yet."
Historic Scotland is due to reach a decision on whether to grant listed building consent within the next few weeks.