From Mitt Romney to Rudy Giuliani: Who are Donald Trump's top five picks for secretary of state?

President-elect Donald Trump is taking his time to appoint a secretary of state – arguably one of the most important positions in his cabinet – leaving the world guessing about who will represent the US on the world stage. Whenever it has looked like the decision is made, another candidate has popped up and thrown the race wide-open. Trump, for his part, seems content to let us wonder a bit longer.

The top five – outlined below by IBTimes UK – are a totally mixed bag. On the one hand you have a former general, David Petraeus, with 37 years in the military and – for better and for worse – a well-established public profile. On the other you have Mitt Romney, a former Republican candidate for president who has branded Trump both a "phony" and a "fraud".

Then you have the two Jo(h)ns: John Bolton and Jon Huntsman, the former a one-time ambassador to the UN and the latter a successful ambassador to China under Barack Obama. The final in our top five is the original candidate, Rudy Giuliani, the former mayor of New York who has made a public bid for the top job but whose keenness may just have turned Trump off.

1. Mr Massachusetts: Mitt Romney

Mitt Romney openly opposed Donald Trump's campaign and was a preferred candidate by many Republicans, but since the election appears to have overcome his differences with the US president-elect. But while many moderates would welcome his appointment, Romney, a Mormon, is hated by the religious right and his appointment to a cabinet position would be extremely controversial.

Despite Romney branding Trump both a "fraud" and a "phony" during 2016, Trump reportedly told aides that the 2012 Republican nominee for president "looks the part". Last month, the former Massachusetts governor was pictured having dinner with Trump at one of his restaurants in New York, the latter smiling and the former looking decidedly awkward.

Speaking after the meeting, Romney said: "He did something I tried to do and was unsuccessful in accomplishing: he won the general election. He continues with a message of inclusion and bringing people together, and his vision is something which obviously connected with the American people in a very powerful way."

In terms of what Romney thinks about foreign policy, Trump supporters are concerned that he is far more aligned with George W Bush-era interventionism rather than the president-elect's more isolationist stance. Romney ran in 2012 on a platform that was wary of Vladimir Putin (the opposite to Trump) and wanted to see a greater US presence in Iraq (again, the opposite to Trump).

Mr Moustache: John Bolton

Of all the candidates for secretary of state, John Bolton has by the far the best facial hair. Unfortunately he is also known to have some unusual friends, once speaking on behalf of an Iranian rebel group called the People's Mujahedin (MEK). Until 2012, the MEK was listed as a terrorist organisation and is hated as much by Iran's democratic opposition as it is by the regime in Tehran.

Bolton has flirted with foreign-orientated office before. In 2005 his nomination as ambassador to the United Nations was blocked by the Democrats and although he was appointed to the position during recess he lasted less than a year, resigning at the end of 2006. He served in George W Bush's administration as secretary of state for arms control and international security.

His views on both Iran and North Korea will certainly play to Trump's campaign playbook. He opposed Barack Obama's nuclear deal with Iran and Bill Clinton's with North Korea. He led the fight to repeal UN resolution 3379, which branded Zionism as racism. Bolton would certainly mark a sea change for US foreign policy. Bloomberg columnist Eli Lake has branded him "the anti-John Kerry".

Mr China: Jon Huntsman

Jon Huntsman is another candidate for secretary of state that was once tipped as a future Republican presidential candidate. The billionaire former governor of Utah ran in the primaries for the US election in 2012 before losing out to another of Donald Trump's suitors, Mitt Romney.

Huntsman is perceived as a bit of a political lightweight, but the events of the past few days may actually improve his chances of landing the job. A former US ambassador to China, Huntsman speaks fluent Mandarin Chinese and may be able to smooth relations with Beijing over the Trump/ Taiwan furore.

Sadly though, Trump doesn't think much of Huntsman's linguistic skills. After the 56-year-old spoke it during the 2012 primaries, the president-elect said: "I didn't think the Mandarin thing worked at all. I thought it was ridiculous." Before calling Huntsman "an Obama plant".

Mr Mayor: Rudy Giuliani

Rudy Giuliani was among the first Donald Trump allies to be linked with the top job, and he has been banging the drum pretty hard since, keen to show the world that he has the credentials to take up what is arguably the most important job in the cabinet. He told the US media that secretary of state was the only role he was interested in taking.

But administration insiders have suggested that the former New York mayor's active public campaigning for the role may have put Trump off. Giuliani has faced searching questions about his international business ties, including revelations that he has earned more than $11m (£8.6m) from lucrative speaking contracts. Trump has heavily criticised Hillary Clinton for doing the same thing.

His firm, Giuliani Partners, has carried out work both with Qatar and the company building the Keystone XL oil pipeline. Giuliani has defended his firm's Qatari work, pointing out that the Gulf country is a US ally, and said that he "has done no work on the pipeline". Like John Bolton, he has also given speeches to the Iranian MEK, which he campaigned to have delisted as a terrorist group.

Mr Military: General David Petraeus

David Petraeus spent 37 years in the military and was once touted as a future president before he was buried in a scandal over his mistress, Paula Broadwell, in 2012. He was later fined $100,000 for sharing classified information with Broadwell, who at the time was his biographer.

Like James "Mad Dog" Mattis, Donald Trump's new secretary of defence, Petraeus served as General Command of the US military, as well as commander of the US forces in Afghanistan. When he retired he was appointed director of the CIA, until being forced out of the role over his affair.

Critics point out that after hammering Hillary Clinton relentlessly during his campaign over her mishandling of classified information relating to her personal emails, it may be a touch hypocritical to appoint a man who was actually convicted of doing so. But the president-elect may take the view that Petraeus has paid his dues for the breach and that his military record is too good to pass up.

His supporters argue that his military experience coupled with his internationalist approach to foreign affairs – Petraeus chaired a Council on Foreign Relations task force that called for strengthening relations between the US, Mexico and Canada – would make him a good counterweight to Trump's bull-in-a-china-shop approach to geopolitics and reputation for isolationism.

"He understood that the key terrain of the conflict was in the realms of politics, diplomacy, and communications, not the use of force per se — although he also did not hesitate to use force in a targeted and effective way," Max Boot wrote in Foreign Policy, while also pointing out that he "has probably been responsible for the deaths of more violent jihadis than any other American"

Petraeus, for his part, seems keen to take the role. Speaking on US TV last week, he spoke out about the scandal that cost him his job. "Five years ago, I made a serious mistake," he said. "I acknowledged it. I apologised for it. I paid a very heavy price for it, and I've learned from it."