The Black Lives Matter protests prompted mosaic artist Tim Cole to resurrect an image he created 12 years ago as a proposed modification of the Sutherland Shire Council logo.
Cole's artwork, which includes a young Indigenous girl alongside Captain James Cook, received a positive response when he contacted councillors last week.
The council will consider whether the logo, which was created in 1906, should also recognise the Dharawal culture.
Cole designed the logo in consultation with two Dharawal elders in 2008 for an exhibition at Hazelhurst Regional Art Gallery and later presented the mosaic to Cronulla Public School, which he attended as a boy.
He has created mosaics with the theme of reconciliation over many years.
For this work, he thought a young Indigenous female provided balance. He approached an Indigenous family at La Perouse on National Sorry Day and received approval from the parents to photograph their daughter so he could use her image.
"The presence of Cook on the logo is fitting and appropriate, but the absence of the Dharawal people is unfortunate," Cole said.
"I look at it is a 'win win'. You keep Cook, but you also acknowledge the Dharawal culture.
"Cook is a great guy, but he was only here for an hour. He's not the full story - he's only half of the story."
Cr Kent Johns has referred the proposal to senior council staff.
"In the current climate, it is something worth looking at and we should at least start the conversation," he said.
It was Cr Johns who suggested naming the new park at South Village Kirrawee after Dharawal woman Biddy Giles, which the community overwhelmingly endorsed in a vote.
Mayor Carmelo Pesce said he was "always open to new ideas", and would wait to see what other councillors thought.
The council's Aboriginal Advisory Committee, headed by Cr Tom Croucher, will discuss the issue.
Cr Diedree Steinwall said, "A new council logo is a matter for the whole community to decide and the input of our Dharawal elders will be invaluable in any consideration of this matter".
In 2001, there was a public outcry when some councillors proposed replacing Cook's image with a dolphin.
The idea was subsequently scrapped.
