Kevin Rudd's hopes for a Steven Bradbury moment – to skate past a contested field of rivals and win the top job at the United Nations – might be on thin ice after Australia's tight election result.

The next step in Mr Rudd's ambition now rests with Malcolm Turnbull and his new cabinet, and a decision on whether to nominate a former Labor leader as a candidate to be the next UN secretary-general.

But such a move risks prompting the ire of the conservative wing of the Coalition in a delicately balanced Parliament.

Foreign Minister Julie Bishop is expected to raise Mr Rudd's possible nomination soon after the new cabinet is sworn in, knowing that for Mr Rudd to be a contender, he will need to join the race soon.

The question was previously informally debated in cabinet before the election, with some ministers personally opposed to Mr Rudd's nomination, while others were more willing to support the principle of backing an Australian in an international job.

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

But the decision does not necessarily need to go to the Coalition party room and close observers warn against underestimating Mr Rudd's standing outside Australia.

"In looking at him as a possible candidate, people should be careful not to have their thinking overly skewed by their views on his time as prime minister or foreign minister," said Richard Rigby, a former diplomat and China specialist.

"He is still received at very high levels in Beijing; he's got a lot of access. Ditto for the United States."

A poll last month by the Lowy Institute for International Policy showed 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.

An earlier survey found his support among Australians as low as one in five.

But the job is not a popularity contest and the nomination from a candidate's home country is regarded as more of an administrative nicety, with the final appointment the outcome of crucial backroom negotiations by the five permanent members of the Security Council.

A total of 12 candidates have so far been nominated by their home countries to be the next UN boss, with the decision expected in the next few months before the incumbent Ban Ki-moon finishes his term in December.

The Security Council will conduct a straw poll on July 21 in New York to whittle down the present field, but other candidates are still expected to come forward.

Mr Rudd has been coy about his ambition, emphasising the UN tradition of rotating the top job from geographic regions, with east Europe yet to have a turn.

There is also a strong push to appoint the first woman to lead the global organisation.

But competition between the US and Russia, another permanent member of the Security Council with a veto, could also stymie eastern European candidates, raising the possibility of a compromise from outside the region.

Mr Rudd has won backing as a potential secretary-general from several global figures, including East Timor independence hero Jose Ramos Horta and climate change guru and economist Nicholas Stern.

When he was prime minister, Tony Abbott penned a letter pledging Australia's support for New Zealand's Helen Clark to be the next secretary-general.

Mr Rudd backed several former political rivals for plum diplomatic postings, including former foreign minister Alexander Downer to be UN envoy to Cyprus and Tim Fischer and Brendon Nelson as Australian ambassadors.

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