Mr Rudd has been openly canvassing global and domestic support for his candidacy for some time and the fraught matter of whether to back him will now go before cabinet, with various government figures understood to be cautious about throwing their support behind the former Labor leader.

"Kevin Rudd has requested that the Australian government nominate him and as [Malcolm Turnbull] has indicated on a number of occasions that will be a matter for the cabinet," Ms Bishop told Sky News.

Immigration Minister Peter Dutton said in April that Mr Rudd was behaving like a pest, and should take up a more normal retirement hobby "and play golf or buy a caravan".

"Kevin was never happy just running Australia. He believed he was always destined to run the world," Mr Dutton said. "Kevin's ego makes Donald Trump's look like a rounding error."

In a statement, a spokesperson for Mr Rudd said the former prime minister "respects the internal processes of the Australian government".

"He also respects the fact that the government has many other priorities at this time, having just been returned to office," the spokesperson said.

"This is a matter for the Prime Minister, the Foreign Minister and their colleagues at a time of their choosing."

Candidates must be nominated by their governments. There are 12 people in the race, including former New Zealand prime minister Helen Clark, former UN climate chief Christina Figueres and several candidates from Eastern Europe, which is due for a stint in the leadership role.

For that reason and the strong desire for a female secretary-general, Mr Rudd's chances have been described as marginal but he believes circumstances can allow him to sneak through the middle. Competition between the United States and Russia and Eastern European candidates hindering each other leaves open the possibility of a compromise outsider.

Opposition Leader Bill Shorten, who served as Rudd government minister and was instrumental in his fall and return, said the government "should put the national interest first and support an Australian", describing his former leader as someone "suitably qualified from his experience in government and on the international stage".

"If it's an Australian government, it will support the Australian. If it's a Liberal government, it won't back the Australian because of petty political reasons. Australians have had enough of that," Mr Shorten said.

Mr Rudd downplayed his chances in April, saying that his view was that "we are likely to have a UN secretary-general from East Europe this time"."Last I looked, my name is not Ruddovich," he joked.

The former prime minister is the president of the Asia Society Policy Institute and holds positions at several other international non-government organisations.

His future at the UN is expected to be raised very soon in a cabinet meeting of the new Turnbull government.

Some conservative MPs and ministers are opposed to Mr Rudd being nominated.

"This guy did his best to ruin our country," South Australian MP Tony Pasin said in April. "That we would think about imposing him on the rest of the world beggars belief."

But he has received public endorsements from prominent figures including UK economist Lord Nicholas Stern and former East Timor president and Nobel prize winner Jose Ramos-Horta.

A recent Lowy Institute poll found Australians are split on whether Mr Rudd would be a good secretary-general, with 46 per cent saying he would and 49 per cent saying he would not.

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