A fundamental problem for Trump is that Greenland is a partially self-governing part of Denmark, and, according to opinion polls, the inhabitants do not want to become Americans. But the US ambition to take over the strategically important, mineral-rich island in one way or another is clear.
Advocacy campaign in support of independence
An independent Greenland would give the United States the opportunity to find a solution directly with the Greenlanders without Danish interference.
The path there is primarily via a Greenlandic referendum - and American attempts to stoke the independence movement are already underway.
Trump has appointed a special envoy to Greenland, and both Vice President JD Vance and the president's son Donald Trump Jr. made high-profile visits to the island last year.
In August, Danmarks Radio also revealed that at least three Americans with connections to the White House had surveyed residents' opinions and worked to establish contacts with politicians and businessmen.
Agreement on free association
In the event of independence, opportunities open up. Since Greenlanders oppose American citizenship, one option is a so-called free association agreement, similar to the agreements the United States has with the Marshall Islands, Micronesia and Palau.
It provides self-government and free trade, while the United States is responsible for defense, financial support, and more.
A White House source recently told NBC News that an association agreement is one of the options being considered.
Pressuring Europe with Ukraine as an ace
Denmark's EU allies have rallied against the US's aggressive rhetoric. But Trump has one card to play that could cause support to waver, Politico, which spoke to a number of diplomats and security experts, reports: Ukraine.
A key issue in the peace negotiations over Ukraine is how secure the US's security guarantees actually would be.
One possible scenario is a package deal - where the Trump administration gives strong guarantees in exchange for an expanded role in Greenland. In practice, the Europeans are then forced to back down in order not to risk, for example, sanctions or the US withdrawing from the Ukraine negotiations.
Military invasion
An American military attack to annex Greenland would likely meet limited resistance at this point.
But the invasion would violate both American and international law, destroy NATO and have consequences that are difficult to predict, Romain Chuffart of the Arctic Institute think tank writes for Politico.
The US would be shooting itself in the foot.
