London (CNN Business) Greenland insists it's not for sale, despite President Donald Trump musing about buying it. But just how much could the world's largest island be worth to America?

Any price tag on Greenland would depend on how desperately the United States wants it and why, and Trump's motivations are unclear.

If history is any guide, the autonomous Danish territory is worth at least $1 billion. In 1946, the United States offered Denmark $100 million in gold to buy Greenland, according to documents in the US National Archives . That's equivalent to $1.3 billion today, taking inflation into account.

Inuit fishermen prepare a net as free-floating ice floats behind at the mouth of the Ilulissat Icefjord.

But even if they wanted to sell, that valuation is unlikely to entice Denmark or Greenland to the negotiating table with Trump.

Past US purchases of other territories could also provide insight into what Washington may be willing to pay. It bought what are now called the US Virgin Islands from Denmark in 1917 for $25 million in gold, equivalent to about $500 million today. It bought Alaska from Russia in 1867 for $7.2 million and the vast Louisiana Territory, stretching from the Mississippi River to the Rocky Mountains, in 1803 from France for $15 million.

"The United States bought Alaska for peanuts in 1867 — about $125 million in today's money. Greenland would be much more expensive to buy at a time of many other demands on the public purse," Iwan Morgan, from the University College of London's Institute of the Americas, told CNN Business.

Morgan said such a deal would involve treaties, legislative processes in Denmark, Greenland and the United States, and likely also the European Union, and he was skeptical it could be done.

"It's not like buying a golf course where you go to an attorney and say 'Can you sanction this?' " he said.

"Even if you got an agreement in principal, the price would be extremely high. If this were to go ahead, it's going to be in the billions, possibly even trillions."

Greenland is already home to the US military's northernmost base, the Thule Air Base, located about 750 miles north of the Arctic Circle. The radar and listening post features a Ballistic Missile Early Warning System that can detect incoming intercontinental ballistic missiles and reaches thousands of miles into Russian territory.

Greenland's untapped oil, gas and minerals may also be attractive to Trump as a race for those resources in the Arctic intensifies.

But Morgan points to legacy as a likely driving force behind Trump's interest.

A NASA research aircraft at Thule Air Base in Pituffik, Greenland.

"This has all the makings of an election issue because there simply is not time to settle the issue before the 2020 race. If he wins a second term, however, he could see a Greenland purchase as a legacy issue and push it harder then."

The Journal also reported that people familiar with the deliberations said Trump's aides were divided on the issue, with some praising it as solid economic strategy and others dismissing it as a passing fancy.

Buying Greenland would certainly not be quick money, according to Tim Boersma, a non-resident fellow at Columbia University's Center on Global Energy Policy.

"In terms of energy and mineral resources, Greenland is a country that is only marginally developed and misses the basic infrastructure to get large-scale projects off the ground," Boersma told CNN Business.

"It's hard to believe that Trump is really that interested in energy and minerals. There's very little exploratory work in Greenland. The conditions are harsh, with most of it covered in ice and snow."