He does have an easier option. A treaty between the United States and Denmark, signed in 1951 at the end of the Truman administration, gives the United States broad rights to reopen the 16 or so military bases that it once had on Greenland.
They were shuttered because Washington thought the era of strategic competition for the Arctic ended when the Soviet Union collapsed. It did not want to pay for frozen bases. So they were left to the winds and the ice: A tour of a few of the old facilities last summer revealed that the long Greenland winters had blown out the windows of the surviving houses and command centers. Runways were broken up into chunks, and overgrown.
But for a few billion dollars — far less than it would cost to buy Greenland outright — the United States has the right to build deep ports, long runways, radar stations and launch sites for missile defense interceptors. It just has not asked. As one senior Danish official put it archly, the country is ready to say yes — which may be why Mr. Trump does not want to raise the issue.