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When he jetted into Russia last month, Kevin Rudd laughed off suggestions he was posing as a freelance peacemaker, trying single-handedly to solve the Ukrainian crisis. Former backers in the Labor Party found themselves awkwardly talking up his skills while also denying he was some sort of special envoy. “He’s not acting as a Labor secret agent to try to fix it,” Bill Shorten said, “although Kevin is a man of remarkable talents.”

However, the former prime minister has now hinted at a behind-the-scenes role in resolving one of the most diabolical security dilemmas in the world, the territorial dispute between Japan and China in the East China Sea.

It was April 10 and Rudd had just regaled a crowded auditorium at the German Historical Museum in Berlin with the parallels between Europe in 1914 and the current security situation in east Asia.

“The challenge of diplomacy now is to take this Senkaku dispute, this Diaoyu Island dispute, from the frontburner of the stove to the backburner, and then off the stove by any creative diplomatic mechanism available to humankind,” Rudd said. “And many of us – officially and unofficially – are working on that as we speak.”

It was vintage Rudd: advanced international wonkery combined with some down-home folksiness, topped off with an oblique reference to how he was engaged informally as a mediator to preserve global peace.

Far from licking his wounds after being dumped by Labor in 2010 and then resurrected briefly last year to lead the party to election defeat, Rudd has dusted himself off and set his sights on a bigger role and a grander stage.

Many in the rarefied world of international diplomacy believe that as he can no longer lead Australia, he now wants to lead the world. Outings like the one in Berlin, hosted by the German foreign minister, are cited as evidence of his ambition.

From Canberra to New York, diplomats are discussing how Rudd is positioning himself to stand for election to the role of United Nations secretary-general when incumbent Ban Ki-moon finishes his second term at the end of 2016.

Since leaving the Australian parliament last November, the former prime minister has crisscrossed the globe, apparently laying the groundwork for his candidacy. Several senior political and diplomatic sources have told The Saturday Paper that Rudd has been approaching foreign governments or their envoys to sound them out about backing his push for the UN leadership.

Rudd’s successor as foreign minister, Bob Carr, has given him a surprise endorsement. “His appeal in a UN contest is likely to be real and potent,” Carr tells The Saturday Paper. “No one is going to work harder on locking in votes.”

But just as Rudd’s initial pursuit of the Labor leadership was long thwarted by the fact he did not belong to a party faction, so too are his international aspirations colliding with the realpolitik of geographic voting blocs in the UN.

Asked directly whether Rudd was pursuing the role, his Australia-based spokeswoman provided the following response: “This is not going to happen. There is a good reason for this. Appointments for the secretary-general of the UN are on a cyclical, geographical basis. The current secretary-general is from Asia. His predecessor was from Africa. Before that, there were secretary-generals from the Middle East and Latin America. And it is agreed that the next rotation will be Eastern Europe, which has never had a secretary-general. Last time I looked, Australia was not in Eastern Europe. For those reasons, Mr Rudd is not a candidate.”

The statement is classic Rudd. There was no denial that he wants it, or that he is pursuing it. The final line echoes Rudd’s language last June, when the then Labor backbencher said, “I am not a candidate for the leadership.” Less than three weeks later, he toppled prime minister Julia Gillard.

1 . Rudd's tour

The conventions and procedures around the election of a secretary-general are almost as opaque as the preselection of Labor senators.

While there is an expectation that it is Eastern Europe’s turn to nominate a candidate, some commentators argue that it is time the quaintly named Western Europe and Others Group, which includes Australia, New Zealand and Canada, had a go. This bloc has not had anyone in the position since Austrian Kurt Waldheim in the 1970s.

There is also the prospect that a candidate from Eastern Europe would not be acceptable to Russia, which has a veto, and that this would open the way for someone who could command the support of all five permanent members of the Security Council, known as the P5.

Tellingly, Rudd’s travels in recent months have focused on the P5 countries – the United Kingdom, France, Russia, China and the United States. Any of these countries can veto a candidate, so he would need to lock in their support.

Further evidence of Rudd’s aspirations appeared to come from his long-time friend and supporter Phillip Adams, who weighed in with a column last weekend, saying he believed Rudd would “do a damn good job in a dammed [sic] difficult role”. Just as he did while calling for Julia Gillard’s resignation and Rudd’s return as prime minister, Adams professed ignorance of Rudd’s intentions.

Carr recalls how Rudd’s attention to international issues won over countries to Australia’s bid for a seat on the UN Security Council.

“Obviously he’s going to throw himself into winning the support of each of the big five, and his record on foreign policy will stand him in good stead,” Carr says. “We basically won the 2012 ballot off the back of Kevin Rudd’s international agenda and the internationalist character it lent Australia.”

In his freshly published Diary of a Foreign Minister, Carr delivers mixed reports on Rudd. He reflects on the warm reception Rudd received from Caribbean nations for his leadership on climate change. If re-elected, Carr writes, Rudd would have diplomatically recognised Palestine, a revelation that could help his UN candidacy among Arab nations. But he also records China’s senior envoy telling him Rudd was loved by some but hated by others in China; that the Commonwealth’s assistant secretary-general Stephen Cutts says Rudd “savaged” him; and that the Japanese recall his tough language on whaling.

John Langmore, who served in a senior role in the UN secretariat from 1997 to 2002, suggests that the former prime minister’s work habits would count against him. Complaints from frontbench colleagues of his micromanagement, disorganisation, lack of consultation and vicious temper would be taken seriously by other countries.

“Of course, he’s a man of great ability but he didn’t seem to learn from being displaced in the most cruel way that he had to become more consultative. There was a secretary-general once, Boutros Boutros-Ghali, who was nicknamed ‘the Pharaoh’. He ran his office in somewhat the same way as Rudd ran his office and excluded everybody else. It drove the secretariat crazy,” says Langmore. “It’s not the secretariat who elect the secretary-general, but they have a lot of influence.”

There are other aspects of Rudd’s legacy that Langmore, now a professorial fellow at the University of Melbourne, says clash with UN principles and would not help his candidacy, notably his decision to increase defence spending while cutting funds for diplomacy, and the deal he struck with Papua New Guinea to banish asylum seekers there.

2 . New York base

If Rudd wants to be considered as a candidate for the UN secretary-general position, he needs to build his support now. Since the sale in the past month of wife Thérèse Rein’s global training and job placement company, Ingeus, for $222 million, the Rudd-Rein family has plenty of resources to underwrite his schmoozing.

Seasoned UN observers say that, from his post at Harvard University, Rudd is well placed to visit New York regularly to court ambassadors to the UN based there. But he has not confined his lobbying to the US.

Despite Rudd’s reputation as a sinophile, the Chinese could present the biggest obstacle to his candidacy. As prime minister, he angered Chinese authorities by raising the sensitive issue of human rights abuses in Tibet while delivering a lecture in Mandarin at a university in Beijing.

It is not unheard of for a UN secretary-general candidate to stand without their country’s support, but it is unusual.

The Saturday Paper understands that the Abbott government would only consider backing Rudd’s candidacy if he could first secure support from all of the P5 countries, thereby demonstrating he had a realistic shot at the role.

The formal contest will unfold during the term of this parliament, so if Rudd’s candidacy progresses, he would need to petition the Abbott government to back him through diplomatic channels.

The Department of Foreign Affairs and Trade routinely facilitates visits by former prime ministers to overseas posts, including organising arrivals and departures, making accommodation bookings and arranging appointments with host governments.

“Consistent with this approach, the department has extended logistics and program support in the past three months to Mr Rudd in New York, Paris, Munich, Moscow and London,” a DFAT spokesman said. “We note the department is not necessarily advised of all overseas travel by former prime ministers.”

In addition to his time in Europe, Rudd has also spent time in China, visiting on at least five occasions since the election last September. The role he assumed at Harvard in February gives him plenty of opportunities to rebuild relationships with Beijing, while at the same time burnishing his credentials among US foreign policy wonks.

Upon his appointment, he said he would be leading research on “a new type of great power relationship” between China and the US, using a phrase that is a pet idea of the Chinese president, Xi Jinping.

3 . Early lobbying

Even before he had even left parliament, Rudd was already paying private visits to world leaders from the opposition backbenches. In October, he met French president François Hollande and his foreign affairs minister Laurent Fabius at the Élysée Palace.

When he arrived in Moscow on March 3, Rudd reportedly asked embassy officials to organise a meeting with President Vladimir Putin’s foreign affairs adviser. Revealing the trip in a story that featured a Photoshopped Rudd in Cossack costume, The West Australian newspaper said the former prime minister also had plans to visit the Ukrainian capital of Kiev, but Rudd used Twitter to deny it.

“In Moscow on trip planned 1 month ago. Never had plans to travel to Ukraine as part of it. Zero arrangements made,” he tweeted on March 5. “Had invite to conference nxt month. No decision to attend. Anything said to the contrary load of old cobblers. But full marks for the pics :)”

When Rudd visited Berlin earlier this month, en route from China, German foreign minister Frank-Walter Steinmeier gave him a warm welcome. Introducing Rudd ahead of his speech at the history museum, the Social Democrat was on familiar first-name terms with the former prime minister. “I know no better expert on east Asia than you,” he said.

Steinmeier, who was about to depart for Japan and China, revealed that the two men had discussed what messages he could relay to the region. They met privately for about half an hour before the presentation, according to the German foreign office.

The audience at the Historical Museum included German politicians and diplomats, as well as Australian ambassador David Ritchie. “His Chinese is not as good as mine,” Rudd quipped, “but his German is fantastic.”

All of this is strategic. Rudd’s campaign to lead the United Nations will depend on years of subtle duchessing. He knows this. On September 7 last year, the night that Labor lost the federal election, he told his supporters: “You won’t hear my voice in public affairs of the nation for some time. That is as it should be.”

Anyone who thought this meant that Rudd had given up on politics after two bruising innings as prime minister underestimated the scale of his drive and vaulting ambition. All he had given up on was domestic affairs.

Watch out world. His name is Kevin. He’s from Queensland. And he’s here to help.