Former Australian prime minister Kevin Rudd has withdrawn his candidacy to be the next UN Secretary-General after current Prime Minister Malcolm Turnbull declared him unfit for the job and refused to back his candidacy.

Mr Rudd was spectacularly ousted as prime minister by his own Labor Party in 2010, with colleagues subsequently alleging that his office was chaotic and he was difficult to work with.

"This is not a partisan issue, this is a considered judgement," Mr Turnbull, who is from the rival Liberal Party, said when announcing the decision in Sydney.

"This is a judgement about Mr Rudd's suitability for that particular role."

The Australian government revealed earlier this month that Mr Rudd, who is based in New York as head of the Asia Society policy institute, was keen to lead the global body.

Candidates must be nominated by their governments and Mr Turnbull said he made the decision not to put Mr Rudd forward after consulting with his cabinet.

Mr Turnbull said he explained his decision to Mr Rudd, who brought Labor out of the political wilderness in a 2007 election landslide, but would not elaborate on his reasons.

"When the Australian government nominates a person for a job, particularly an international job like this, the threshold question is, 'Do we believe the person, the nominee, the would-be nominee, is well suited for that position?'" he asked.

"My judgement is that Mr Rudd is not, and I've explained to him the reasons why."

Mr Rudd, who was dumped as prime minister by his colleagues in 2010 for Julia Gillard only to be reinstalled briefly as Labor faced an electoral wipeout in 2013, had the support of Mr Turnbull's Foreign Minister Julie Bishop.

Labor had also argued it was in the national interest to have an Australian in the role but reports said there was little enthusiasm for him within the government.

Mr Rudd's office said he would not continue with his candidacy.

"A nomination by the government would not have granted Mr Rudd a position. It would simply have enabled him to stand alongside the 12 other candidates from across the world, and compete on his merits," the statement from his office said."That is now not to be."

After months of public campaigning, debates and open hearings, Security Council ambassadors must decide who will succeed Ban Ki-Moon at the world body from 1 January.

Among the top contenders are Argentina's Foreign Minister Susana Malcorra, Slovenia's ex-president Danilo Turk, New Zealand's ex-prime minister Helen Clark and Antonio Guterres, who served as Portugal's prime minister and headed the UN refugee agency.