Donald Trump has made clear that he wants the United States to take Greenland.

In the wake of the special forces operation to bring Venezuelan President Nicolás Maduro to the US to face drug trafficking and weapons charges, Mr Trump has repeatedly told reporters the US "needed" the territory for security reasons.

Experts say Greenland's location makes it key for American ambitions to have sovereign hemispheric domination, with its extensive rare earth and oil deposits an added bonus.

But while the massive but sparsely populated Arctic island is in many ways self-governed and has ambitions of becoming fully independent, it's still a Danish territory.

So how can the US go about achieving the president's goal?

At least three possible options have been floated: military action, a purchase agreement and the formation of a Compact of Free Association.

Experts say Denmark would be unlikely to resist a military annexation of Greenland. (Reuters: Guglielmo Mangiapane)

'Short and sharp'

While the idea of the US invading Greenland may seem far-fetched, the Trump administration has repeatedly refused to rule it out.

"The president and his team are discussing a range of options to pursue this important foreign policy goal, and of course, utilising the US military is always an option at the commander in chief's disposal," government spokesperson Karoline Leavitt said in a statement to AFP.

In the "unimaginable" event that it did go ahead, experts say a US invasion of Greenland would be "very short and sharp".

The US military vastly outmatches Denmark's in size and technological capability and already has a base on the island it could use as a beachhead.

Donald Rothwell, professor of international law at the ANU College of Law, said Denmark's military capacity to resist the United States would be "very limited".

"I just can't see Denmark wanting to militarily resist in any significant way because — this is unimaginable — but there is an ultimate threat that the United States could launch strikes against Denmark itself, on Copenhagen," he said.

"I just can't see a Danish prime minister wanting to even allow the possibility of that to eventuate.

"So any military confrontation would be very short and sharp."

While taking Greenland might be militarily trivial, it would be a breach of international law and the diplomatic costs would be enormous, potentially permanently fracturing America's long-standing relationships in Europe — and the rest of the world.

Danish Prime Minister Mette Frederiksen said on Monday it would be the end of "everything".

"If the United States decides to militarily attack another NATO country, then everything would stop — that includes NATO and therefore post–Second World War security."

Mette Frederiksen says an invasion of Greenland could end the NATO alliance. (AP: Geert Vanden Wijngaert/File)

The 32-member North Atlantic Treaty Organization (NATO) of North American and European states was established in 1949 around a commitment to collective self-defence, initially against the Soviet Union.

European leaders responded to Mr Trump's remarks by rallying around Denmark, saying Greenland was owned by its people.

A German government source told Reuters this week that Germany was "closely working together with other European countries and Denmark on the next steps regarding Greenland".

Professor Rothwell said military action would be an "absolute red line" for many of the US's key partners in Western Europe — one the US would be hesitant to cross.

"Even the United States probably can't do without the UK, certainly, and France," he said.

"And my own sense is it could even be a red line for Australia in terms of using force against Indigenous peoples in a small, unprotected territory which is completely peaceful.

"I think that that could really create a real fracture in terms of the US–Australian relationship.

"So that's why I think that for a whole series of reasons, the military force is sort of bluster, rhetoric coming out of the White House."

Stuart Rollo, from the University of Sydney's Centre of International Security Studies, said the Trump administration's refusal to rule out military action was likely a bargaining tactic.

"I think it ties in very much with Trump's general mode of practice, which is to take a maximalist aggressive position and then use that as a basis for negotiation," said Dr Rollo.

"I'm sure the US doesn't actually want to militarily take Greenland but I think they're very comfortable making the threat, with the intention that from there all of a sudden the purchase of Greenland looks relatively attractive — if those are the options."

Indeed, Secretary of State Marco Rubio has reportedly continued to insist privately that Mr Trump planned to "buy" Greenland rather than invade it.

Could the United States buy Greenland?

So how realistic is it that a country could just buy a territory like Greenland?

Susan Stone, Credit Union SA chair of economics at Adelaide University, said purchasing territory was common back in the 19th century.

"The US was one of the most prolific in this area," she said.

American acquisitions included the Louisiana Purchase from France in 1803, some of what's now Arizona and New Mexico from Mexico, Florida and the Philippines from Spain, the Virgin Islands from Denmark and Alaska from Russia in 1867.

The US even sought to purchase Greenland in 1946 during the Cold War but was knocked back.

Dr Stone said territorial purchases had become less common because the practice was not generally consistent with values of democracy and self-determination without the consent of the Indigenous people or residents.

Nonetheless, Dr Stone said a deal still could be done.

"Willing buyer, willing seller, it is possible," she said.

"Theoretically, if Greenland … and Denmark agree to a sale, then they could go ahead and do it."

The biggest hurdle was that Greenland did not appear to be for sale, she said.

"Right now, what's coming out of Greenland is that they are not interested in being sold to the United States."

If the US could convince Greenland and Denmark to sell — one way or another — Dr Stone said working out a price would also be difficult.

She said it would need to take into account factors like the territory's GDP, the future earning potential of its mineral assets such as rare earths and oil, the population's human capital, geo-strategic value and other intangible benefits.

The United States and the Pacific Island nation Palau have a Compact of Free Association. (Reuters: Jackson Henry)

What is a Compact of Free Association?

Some have suggested a compromise could see Greenland forming something called a Compact of Free Association with the United States.

Professor Rothwell said a Compact of Free Association was one of a number of forms of legal and constitutional arrangements the US had with territories known as "insular areas".

"That's important because it needs to be noted that there are already existing models that could be applied under US law, of which one is the Compact of Free Association," he said.

Under Compacts of Free Association, the Federated States of Micronesia (FSM), Republic of the Marshall Islands (RMI), and Republic of Palau all have their own governments but the US has responsibility for their defence and foreign affairs.

New Zealand has similar free-association arrangements with the Pacific Island nations of Cook Islands and Niue.

"The Cook Islands could be a particularly relevant one because the Cook Islands has developed a fairly robust position in terms of its governance and its independence, so to speak," he said.

Greenlanders have shown little interest in becoming a US territory but some believe Donald Trump's interest is an opportunity. (Reuters: Sarah Meyssonnier)

Greenland would have to be independent to make a pact with the United States.

However, the territory is already well along the road, having achieved "home rule" in 1979 and greater self-governance in 2009.

Greenland's government has a stated goal of full independence, which Denmark has said it will grant following a successful referendum.

Surveys have indicated that a majority of Greenlanders do want full independence, but are not interested in becoming a part of the US

However, a poll of about 500 residents last January found that while 45 per cent saw Mr Trump's interest in the territory as a threat, another 43 per cent saw it as an opportunity.

An anonymous senior US official told Reuters this week a Compact of Free Association was one of the options Mr Trump and his advisers were discussing.

It's not the first time the idea has been flagged.

Last year, former US National Security Council chief of staff Alexander B Gray told Nine's 60 Minutes program a Compact of Free Association or some kind of arrangement like the US had with Puerto Rico or the Virgin Islands would be a "very good option".

Mr Gray said the US could provide Greenland with economic opportunities and security.

"I think their sovereignty and their sovereign right to self-determination has to be first and foremost on everyone's minds," he said.

"But the good news for us is I think that what we offer as the United States is much more compelling than what the Russians and the Chinese have to offer."

In February last year, VOA reported that representatives from Greenland's government in the US had met with the Federated States of Micronesia's ambassador to the US to learn more about their Compact of Free Association with the US.

The Greenland government at the time refused to comment on the meetings.

Professor Rothwell said one valid option would be for the US to negotiate such an agreement with Denmark, which would make appropriate consultations with the existing government in Greenland.

"The second option would be one in which Denmark, in consultation with the Greenlanders, accelerates Greenlandic independence … but in the process, alongside that, negotiates an arrangement with the United States in which it would acquire free association status," he said.