The building has been closed for two years after it was declared unsafe.
The film's producers want to use the main entrance for around six weeks as a location when filming begins in July.
Campaigners have arranged for engineers to survey some of the damage around it but hope work could enable the foyer and main hall to stay open.
Ian Hill, the director of Save The Coal Exchange, said any remedial works would allow the building's front entrance, foyer and main hall to continue to be used once The Crow has finished filming.
"We are taking the opportunity to make sure that when the door opens, it stays open," he said.
"The Crow will be on site for around six weeks. When they leave, we hope to be able to keep the front door open, and give the public access to the foyer and main hall."
The fee paid by the film's producers should cover the cost of making the entrance safe. The Crow will be shot on location in south Wales, and at the Pinewood Wales studios in Cardiff.
The owners of the Coal Exchange went into liquidation last year, with around £5m currently owed to Cardiff Council and two banks.
The building is considered to be one of the capital's most significant historical landmarks, and was the place where the first ever £1m cheque was signed. In recent years it had been used as a concert venue and office space until its closure in 2013.
Discussions have already begun with the hope of transferring the ownership of the Coal Exchange to the charity which is campaigning to save the building.
It plans to raise around £15m to fund the restoration of the building over the next three to four years, if the initial works are successful in partially reopening the venue.
THE COAL EXCHANGE - TIMELINE
Actor Jack Huston is widely reported to be in talks to take on the lead role in The Crow, which will be filmed at Pinewood studios on the outskirts of Cardiff.
It will be the first multi-million pound A-list film to get made at the new facilities.
The original 1990s film starred Brandon Lee, who died on set after being accidentally shot.
The Hollywood remake of The Crow, which will be filmed in south Wales this summer, could help reopen Cardiff's historic Coal Exchange.