Greenlanders have a message for Donald Trump following reports the US President has repeatedly inquired about buying the autonomous Danish territory: Not gonna happen.

In the small village of Kulusuk, a settlement off Greenland's southeastern coast, locals responded icily to news that the White House counsel's office has looked into the possibility of purchasing Greenland from the Danish government.

"They tried to buy us in 1867, during Second World War, and now they are trying again," local Kulusuk resident Bent Abeelsen told CNN. "Not gonna happen."

The sentiment was echoed by the island's government, which said in a statement Friday: "Greenland is not for sale."

But at least one bemused Kulusuk local said he was open to the idea of what America could offer Greenland.

"I think it's a funny offer but who knows. That's always like that with him. At first nobody thought he was going to win, right? So we'll see," Kunuk, who declined to give his last name, told CNN.

Asked whether he would want to be an American, Kunuk said: "That depends on what it gives me. I like American movies and American music, and I wouldn't mind cinemas and swimming pools here. Some infrastructure would be good."

As Abeelsen pointed out, Trump would not be the first American to try buy Greenland. Though President Harry Truman dodged questions about his pursuit of control in the region, the United States allegedly tried to buy Greenland in 1946, and in 1867, Secretary of State William Seward showed interest in purchasing the island.

Trump's interest in the island -- first reported by The Wall Street Journal on Thursday -- speaks to its military and research potential. The territory is home to Thule Air Base, the US military's northernmost base, located about 750 miles above the Arctic Circle and built in 1951. The radar and listening post features a Ballistic Missile Early Warning System that can warn of incoming intercontinental ballistic missiles and reaches thousands of miles into Russian territory.

In remote areas like Kulusuk, Greenland's geopolitical significance might seem less obvious.

The village subsists mostly on tourism and local fishing. Unemployment is high and the population has been in decline for a while. It currently stands at around 280 people.

The country's Ministry of Foreign Affairs took the opportunity Friday to promote tourism to the sparsely populated island, which is becoming more green due to the climate crisis. Greenland's ice sheet has experienced unusual levels of ice loss this summer, spurred by soaring temperatures in the Arctic. It shed 2 billion tons of ice in just one week in June.

"#Greenland is rich in valuable resources such as minerals, the purest water and ice, fish stocks, seafood, renewable energy and is a new frontier for adventure tourism," Greenland's MFA said on Twitter. "We're open for business, not for sale."

A cartoon in one of Denmark's major newspapers, Politiken, quipped in a faux real estate advertisement that Greenland's selling points included: only one previous owner, beautiful land in a quiet area, newly renovated, self-sufficient, can be used all year round, good fishing opportunities and no neighbours.