The Victorian government has rejected a plan to rename the Yarra River to recognise its traditional owners, saying the name remains an “icon”.

The City of Melbourne Council proposed to consult with Indigenous stakeholders on the prospect of changing the name, which would have seen the Wurundjeri name "Birrarung" being officially used for the river.

The proposal was recently floated by the Yarra River Business Association, which has been looking at ways to rejuvenate the river precinct.

Acting Lord Mayor of Melbourne City Arron Wood said it was crucial that Aboriginal stakeholders were engaged before the idea went any further.

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"One person, a non-Aboriginal person, may not think the changing of the name is that important," he said.

"What we do know is that it’s a real sign of respect to our Aboriginal community.

"Really what we should be doing is taking advice from them on any name changes."

Mr Wood said the council would be consulting with the Aboriginal community.

"We’ll work through those processes… it’s really critical that we hear the Indigenous voice on this one," he said.

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But acting Victorian Premier James Merlino dismissed the idea, saying the government had already taken steps to ensure the river's Indigenous heritage was recognised.

“The Yarra is an icon of Melbourne [and] it’s close to Victorian’s hearts,” he told The Australian.

“We’ve done a lot to protect the heritage of the Yarra, to protect its indigenous and cultural importance.”

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“We set up statutory authority the Birrarung Council to protect the heritage of the Yarra River into the future. We’ve got no plans to change the name.”

It's unknown what steps the council will take next, following the state government's comments.

Surveyor and explorer John Wedge coined the Yarra name in the mid-1830s after asking the local Wurundjeri people what the river was called.

Legend has it Mr Wedge misheard the reply of "Yarro-yarro", which roughly means ever-flowing, and instead coined the name "Yarra Yarra", which means waterfall.

Asked whether a possible name change could have a negative impact on tourism, Mr Wood said many people were actually drawn to areas with a strong sense of Aboriginal history.

"Perhaps this change in naming certain places after their Aboriginal names is something that our tourists are actually going to embrace," he said.

Mr Wood stressed that, before anyone got carried away with the proposal, it still wasn't clear whether Aboriginal leaders supported the name change.

"We don’t know whether or not this push is supported by the Aboriginal community," he said.

"But any suggestion around this I think it is important to have a look at, to consult with Aboriginal leaders and consider it on its merits."