The New Yorker looks at Trump’s expressed interest in Greenland, asks is his interest real, and concludes it is. They note:
Last week, Denmark’s foreign minister said that his government was “open to dialogue” with the United States on how the two countries could coöperate in the Arctic region, including Greenland. “I presume the idea is not to start a war or to invade,” Vidal said. “But over time there could well be significant economic and military deals that would bring Greenland a lot closer to the United States. That is the most likely outcome, in my opinion.”
Florian Vidal is a scholar at the Arctic University of Norway who specializes in polar geopolitics. This is one view, obviously there are others.
For example I can imagine Greenland signing with the U.S. a "compact of free association" (aka COPA) similar to those we have with the Federated States of Micronesia, the Republic of the Marshall Islands, and the Republic of Palau.
