Washington (CNN) Forget a "Team of Rivals." This would be a double act of denouncers.

The thought that Mitt Romney would ever join the Cabinet of Donald Trump -- given their hostility, mutual contempt and venomous rhetorical exchanges -- might be the most absurd notion yet of a crazy political year.

But the possibility that Trump and the man he labeled a "choke artist" could find common cause in the new administration was nonetheless a hot topic ahead of their meeting Saturday at the President-elect's Bedminster, New Jersey, golf retreat.

The 2012 Republican nominee, who once warned in a CNN interview that a Trump presidency would mean "trickle-down racism" and "trickle-down bigotry" instead sat down with Trump and discussed the job of secretary of state, an appointment that would make Hillary Clinton's decision to serve in the same post under her 2008 primary rival Barack Obama seem routine in comparison.

After the meeting, Romney offered no hint as to whether he was offered or would accept a role in Trump's administration.

"We had a far-reaching conversation with regard to the various theaters in the world where there are interests of the United States of real significance. We discussed those areas and exchanged our views on those topics," Romney said in brief remarks to reporters. He did not take questions.

Vice President-elect Mike Pence confirmed Sunday that Romney is under "active consideration" for secretary of state.

"The President-elect was very grateful that Gov. Mitt Romney came in. They had a good meeting. It was a warm and substantive exchange. I know he is under active consideration to be secretary of state of the United States along with some other distinguished Americans," Pence said on "Fox News Sunday."

But the possibility that Trump and the man he labeled a "choke artist" could find common cause in the new administration is a hot topic after their weekend meeting at the President-elect's Bedminster, New Jersey, golf retreat.

On Sunday night, a Trump transition source said the selection of Romney as secretary of state is "possible."

Intrigue surrounds meeting

Prominent members of Romney's orbit, while not confirming that the former Massachusetts governor is interested in running US diplomacy, are not entirely dismissing the notion that he could agree to serve.

"One of the things that drives Gov. Romney is a sense of duty, and I think that sense of duty is what's driving him to help President-elect Trump in any way he can as he puts together a government," Kevin Madden said Friday on CNN's "New Day." "I think he recognizes that there is that type of outreach going on with President-elect's transition team."

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On the face of it, there are plenty of reasons why the 2012 nominee would refuse to serve alongside Trump, not least because of their sharply different characters and positions on some key foreign policy issues.

But there are enough reasons why it might make sense for both men to lend their meeting plenty of intrigue.

For the President-elect, Romney would bring an immediate burst of knowledge, global credibility, sound temperament and competence to his nascent administration.

His selection would also be seen as a genuine gesture to bind the wounds in the Republican Party and the foreign policy establishment left over from a bitter primary campaign.

It could also open the floodgates for the kind of credible, experienced GOP foreign policy insiders whom Trump needs to staff crucial, lower-ranking national security jobs to join the administration.

And since Trump's core voters are more concerned with "draining the swamp" of well-known Washington insiders than foreign policy, the State Department may be one place he could put an establishment figure and not sustain much political damage.

"Mr. Romney would be a great choice in a sense that would be a signal sent to moderates as well as conservatives," William Cohen, a former US defense secretary, told CNN International's Hala Gorani on Friday.

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"Whether that is a realistic thing remains to be seen -- I am skeptical but nonetheless remain hopeful that such an appointment, or people like Mitt Romney would be considered."

Some of Romney's closest advisers initially expressed surprise at the news that the two men would meet. But some told CNN's Gloria Borger that the former venture capitalist prized his duty to his country above all else. Others noted that though he is known as a businessman, Romney's true interests centered on foreign policy, and that secretary of state would be the only Cabinet position he would accept. Another friend however expressed extreme skepticism Romney would join the Trump Cabinet.

Romney could be relief to US allies

For sure, a Romney appointment would come as a great relief to US allies who are deeply anxious about the direction of Trump's foreign policy, and who see alternative names floated for secretary of state such as Rudy Giuliani and John Bolton with much greater apprehension.

That's because Romney is squarely within the parameters of accepted US foreign policy orthodoxy, is an internationalist, is well-known abroad and is committed to the notion of free trade, US alliances and a robust US posture in the world.

Trump on the other hand has raised doubts about the bedrock pacts of the international system such as NATO and US alliances in Asia, is yet to define his "America First" creed and has spooked Eastern European allies with his praise for Russian President Vladimir Putin.

Trump's temperament and a campaign in which opponents said he was unfit to control the nuclear codes also alarmed foreign policy elites and governments abroad -- so the thought of someone as sober and self-controlled as Romney beside Trump in the Situation Room would calm some nerves.

The former governor would sail through Senate confirmation, thanks to his reputation as a devoted and devout family man with no personal skeletons.

No one can know what is in Romney's mind. But Saturday's meeting was not one he had to take. After all, it carried the risk that the President-elect is simply using his good name to give the impression that he is casting a wide and conciliatory net across his party as he chooses his Cabinet.

Career capper

But were Trump to offer him the job of secretary of state, it's not impossible Romney would accept.

It would be one last chance to serve and cap a career that once seemed headed for the pinnacle of national politics and at least would partially make up for the disappointment of his loss to Obama four years ago.

Given Trump's lack of experience in foreign policy, and a leadership style that promises to be heavily reliant on his subordinates, Romney could see the chance of wide autonomy in setting US foreign policy as attractive.

It might also be a good fit with the Mr. Fix-it brand of the former venture capitalist who rescued the 2002 Salt Lake City Winter Olympics.

Still, there's a reason why a Romney nomination as secretary of state would be seen as yet another shocking development in 2016.

Trump eviscerated Romney on the campaign trail. He said he was a "disaster as a candidate" who "choked like a dog" and said he had a lot of friends -- but Romney wasn't one of them.

But maybe Trump appreciates someone who can throw a punch. After all, Romney warned Trump was a "phony," a "fraud" who was playing the American public for "suckers" and once said he wanted to be able to look his grandchildren in the eye and say he took a stand against the GOP nominee.

Would Romney be allowed to speak for the President?

Even if the two men put personal animosity aside, the starchy Romney would be an incongruous figure in a team that includes firebrands such as new White House adviser Stephen Bannon and the next national security adviser Michael Flynn.

And even if Trump gave him broad latitude to dictate US foreign policy, Romney would be taking a risk that the 45th President's intemperate public comments and volatile personality would undo painstaking diplomatic work.

There is nothing more debilitating for a secretary of state than the view around the world that he or she does not speak for the President or is on a different page.

Similarly, Romney might also face having his own words turned against him in talks with a foreign power since he said this year that the President-elect's promises were "as worthless as a degree from Trump University."

Romney and Trump would begin any partnership estranged in some key areas of policy. The former Massachusetts governor is a committed free trader for example. He warned in 2012 that Russia represented the top geopolitical threat to the United States. Trump has meanwhile warmly praised the leadership of Putin and promised to ease rocky relations with the Kremlin.

Still Trump and Romney do agree on the need to battle Islamic extremism, the magnitude of the threat from terrorism and the need to hike military spending.

Lanhee Chen, a top aide to Romney in 2012, argued that though there were differences on trade, the gaps were perhaps not as wide as they might seem.

"I do think there is some similarity in a focus on American interests that both Gov. Romney and I think Donald Trump expressed on the campaign trail," said Chen, a CNN contributor.

"If you look at the atmospherics, the macro level, there may actually be more there than meets the eye in terms of commonality between things that Donald Trump has expressed and Gov. Romney has expressed."