A federal minister has suggested Australia could move towards becoming a republic within a decade, thus ensuring a new Australia Day anniversary to replace the controversial January 26 celebrations.

Indigenous Turnbull Government frontbencher Ken Wyatt has proposed the solution, as debate again rages over whether it is appropriate to celebrate Australia Day on the anniversary of the arrival of the First Fleet.

The official Australia Day website acknowledges the sensitivities of the symbolism for Aboriginal and Torres Strait Islander Australians who "see it as a day of sorrow and mourning".

Mr Wyatt has proposed a long-term plan to deal with those concerns.

"I think that within this next decade momentum will grow for Australia to have serious discussions about becoming a republic," Mr Wyatt said.

"I think we will be ready then to shift the date to the day we become a republic."

Mr Wyatt has also warned against letting the issue overtake this year's Australia Day events.

"I'm not suggesting we kick this can way down the road, but I'm suggesting we don't allow the emotive argument to take over the reasons for which we celebrate this day," he said.

"I think it would be a great way to celebrate not only the old, and to acknowledge our past, but to acknowledge a new direction we choose as a nation of people."

Mr Wyatt first raised the proposal in Fairfax Media this morning.

Prime Minister Malcolm Turnbull and Opposition Leader Bill Shorten have both publicly stated that they support the status quo, keeping Australia Day on January 26.

Today Mr Shorten said he still wanted to see public discussion about the date and he accused the Prime Minister of "sneering" at Aboriginal people who want to debate the issue.

Mr Turnbull was the unsuccessful face of a push for the nation to become a republic in 1999.

The referendum failed at that stage, but Mr Wyatt argues it is only a matter of time before it is back on the public agenda.

"Australia will invariably determine its own pathway, the same as Canada did," he said.

Wyatt questions cost of extra holiday

Mr Wyatt has also questioned the expense of another solution offered by Indigenous Labor frontbencher Linda Burney.

This week Ms Burney suggested a separate day be set aside across the country to celebrate Indigenous Australians.

Reconciliation Day is already in place in the ACT.

"We've got to consider in the context of our economy, whether we can afford to have a day set aside," Mr Wyatt said.

He noted the suggested option of replacing the Queen's Birthday public holiday would not go down well with staunch monarchists.