Cabinet secretary Arthur Sinodinos has cast doubt on whether former prime minister Kevin Rudd will get Cabinet's backing for his bid to become United Nations secretary-general.

The Australian Government would have to formally nominate Mr Rudd for the Security Council to consider him as a candidate.

"It's funny, isn't it? 2016 and we're still talking about Kevin, you know which I think he would love, he loves the idea we're talking about him," Senator Sinodinos said.

He said Cabinet would discuss the issue during one of its next two meetings.

Speculation mounted for months over whether Mr Rudd would run to be UN leader. ( ABC )

"I'm not spilling any secrets to say there would be a lot of people on our side of politics to say they have reservations about supporting Kevin," he said.

"The politics of that era are still pretty raw and the idea that he could be on the world stage seeking to overshadow Australia in other ways does grate with some of my colleagues."

The first of what are called United Nations Security Council straw polls has already taken place, with former Portuguese prime minister Antonio Guterres emerging as the favourite.

Mr Rudd has also attracted criticism from his side of politics.

Former Labor New South Wales premier Kristina Keneally described him as a psychopathic narcissist on Sky News last week.

"I can think of 12 Australians off the top of my head who would be a better Secretary-General and one of them is my labrador, so let's be blunt here, she has a lot more empathy than Kevin Rudd," Ms Keneally said.

Kiwis line up to attack Rudd

The former prime minister is also attracting criticism from the other side of the Tasman.

Former New Zealand Labour prime minister Helen Clark is an announced candidate in the race for the UN's top job and current Prime Minister John Key has started criticising Mr Rudd to support her.

Mr Key, a one time rival to Ms Clark, told NewsHub: "New Zealanders and I reckon a hell of a lot of Australians know who the best candidate is."

Mr Key has texted Ms Clark since the first straw poll, which shows there are five candidates ahead or tied with her, to work on a "game plan".

He told TVNZ Ms Clark was "world class" and the UN should pick her to be its first female leader.

New Zealand deputy Labour leader Annette King has not always been a supporter of Ms Clark's and once challenged her leadership, but has now joined her UN cheer squad and talked down Mr Rudd's chances.

"If there is a mind to look at a secretary-general from our side of the world, Helen Clark is head and shoulders above anybody else," she said.