Prime Minister Malcolm Turnbull reportedly dismissed formal advice from the Department of Foreign Affairs and Trade saying Kevin Rudd was “eminently qualified” for a tilt at the UN’s top job.

Mr Turnbull has said the government would not back the former Labor prime minister because he believed he was “not well suited” for the role.

DFAT's submission, presented by Foreign Minister Julie Bishop, said Mr Rudd compared well with the current field of 12 candidates, and was a better candidate than previous secretary generals who held the job, The Australian reports .

Ms Bishop argued in favour of nominating Mr Rudd.

Thirteen Indigenous leaders also tipped their support to Mr Rudd, putting their names on a statement saying he is “suitable” for the job.

“The man who delivered the apology is a man suitable for the post of secretary-general of the UN,” the statement said.

One-time environment minister and rock singer, Peter Garret, took aim at Mr Rudd during a performance in Brisbane on Friday night.

“We dodged a bullet, now that Rudd’s not gonna be ­secretary-general,” he said.

Deputy Prime Minister Barnaby Joyce told the paper the issue is one of “personality versus protocol”.

“The assessment by so many of Mr Rudd’s former colleagues basically ruled him out,” Mr Joyce said.

Meanwhile a former Australian ambassador to China who served under the Rudd and Gillard government, Geoff Raby, says Mr Rudd's bid might not be over.

Mr Raby pointed out Mr Rudd was close to US Democrats presidential nominee Hillary Clinton.

In an opinion piece for the Australian Financial Review he speculated that Mrs Clinton could back him for the job, if she wins the US election.

Trade Minister Steve Ciobo denied the decision set a precedent.

"The reasons the prime minister harboured reservations have been laid out by the prime minister and I'm comfortable with it," he told ABC radio today.