Port Adelaide's Fishermen's Wharf Market building could be on borrowed time, following an application by its owner to demolish the waterfront building.

The wharf shed is located next to the lighthouse and is a popular spot with locals, attracting thousands of people to its Sunday market.

Port Adelaide Enfield Mayor Gary Johanson said owner and property developer Hans Ehmann made the application to the Port Adelaide Development Assessment Committee, which is part of the state's Development Assessment Commission (DAC).

Mr Johanson said while the final decision is largely out of the council's hands, he would be sad to see the building go and hopes it can be saved.

"Five to 10,000 people I believe every Sunday go to that market," he said.

"It supports many people that have a passion to not only show off their wares and have a little bric-a-brac stall, it gives a certain character to the port because it's people meeting people."

The Port of Adelaide branch of National Trust SA condemned the proposal in a public letter addressed to Premier Jay Weatherill, Urban Development Minister Stephen Mullighan, Port Adelaide state MP Susan Close and federal MP Mark Butler.

"We express our shock and concern that there is an application to demolish [the building]," the letter stated.

"It is the last remaining wharf shed in the inner harbour and spans the era of bulk cargo handling through to containerisation."

National Trust branch co-chair Pat Netschitowsky said she hoped the building could be reused instead of being ripped down.

"Our hope would be that it could be redeveloped but that they would use the existing building so that you retain some fabric and character of Port Adelaide," she said.

"We feel like we've lost a lot of the heritage and character already so we're very keen to retain [it].

"It's an iconic building, it's in a very central part of Port Adelaide where thousands of tourists come and they catch the tourist boats to go for trips down the river."

Hoping for a compromise

Mr Johanson said he hoped Port Adelaide Enfield Council could work with the Government and Mr Ehmann to reach a compromise.

"I think there is a place for this building even if it was to be demolished," he said.

"There is ample land between the aviation and the rail museum where a building like this could be deconstructed and reconstructed. It's not impossible. They're designed basically to be moved like that, these type of buildings."

A Government spokesperson said the future of the site would be a "matter for independent assessment by [the] DAC before any recommendation is made".