But they are not destined for the tip, instead they will be kept by the memorial as part of their art collection.

Among the 26 stone gargoyles of native animals lining the courtyard at the Australian War Memorial, sit two depicting faces of an Indigenous man and woman – which critics have long labelled "bizarre" and "racist".

The memorial is now asking for bids to remove the 26 gargoyles and replace them with 24 newly carved animal ones using 3D images, mimicking the original style and construction.

Crucially, the current tender does not include a request for two new "indigenous gargoyles" and instead proposes community consultation be undertaken to decide whether or not to replace them.

Assistant Director of the National Collection Tim Sullivan said the memorial was consulting with heritage specialists and Indigenous stakeholders to determine the fate of the 26.

"The eventual outcome of the reconstruction work will be determined by this consultation," he said.

The tender claims the aim of the project is to clear away attached building materials infected with asbestos, and improve the drainage they were designed to provide for the building.

"The reconstruction project aims to improve visitor safety by replacing the asbestos-containing mastic sealant used in the 1970s with an appropriate mortar," Mr Sullivan said.

However, he confirmed the memorial had been aware since mid-2012 of the bonded asbestos, which is safe if not disturbed.

Mr Sullivan also outlined what would be done with the existing sculptures.

"The gargoyles are part of the Memorial's art collection, and as such, will remain so after the conclusion of the work," he said.

The project would "restore the appearance, historical integrity and functionality of the Memorial's Commemorative Area".

The Indigenous face gargoyles have long been the subject of criticism over the years including from Aboriginal elders.

Ngambri traditional owner for the Canberra area Matilda House said the removal of the Aboriginal head gargoyles would be "good riddance".

"Who would want to have things up there? Why would we want to have a garden with heads that people are calling Aboriginal gargoyles?

"For heaven's sake, [it's] disgraceful," Ms House said.

Historians too have questioned their existence.

Charles Sturt University Adjunct Senior Lecturer Dr Robin McLachlan, who worked at the memorial in the 1990s, said it had been a "very sensitive" issue when he decided to used it as an example in his public history course at CSU.

"It's a contest between preserving the integrity of the building that is a very important monument for Australia and removing something which is blatantly racist.

According to Dr McLachlan there has long been internal angst at the AWM over the gargoyles' future.

"There was an ongoing uneasiness about what to do with them," he said.

Back in 1996, Dr McLachlan questioned officials at the memorial over whether they were embarrassed by the sculptures, but they rejected the idea, telling Dr McLachlan that "the Memorial has no desire to deflect public attention from them".

Apart from the memorial getting slammed over the sculptures, there have long been calls for separate memorials to remember indigenous soldiers and more acknowledgement of the frontier wars.

Specifically, the latest push from the inside has been for a separate monument specifically to Indigenous personnel close to the grounds of the memorial.

Ms House said she too would support a new monument for Aboriginal soldiers.

The stone gargoyles in the commemorative courtyard were originally designed by sculptor Leslie Bowles and carved from plaster casts by Mr W. Swan in 1941.

The memorial has specified they wished the new gargoyles, along with the new stonework string course that is also part of the tender, to be made from Wondabyne sandstone.