Trump has with "varying degrees of seriousness" expressed an interest in trying to purchase the icy 811,000-square-mile island in the North Atlantic, according to The Journal, citing unnamed sources familiar with the deliberations.
Greenland is an autonomous Danish territory with a population of more than 50,000 and has natural resources such as coal and uranium. Trump reportedly told advisers in one exchange last spring he'd heard that Denmark was having financial problems because of the subsidies it pays to Greenland, and wondered if he should buy it. "What do you guys think about?" Trump asked the room, a source told the Journal. "Do you think it would work?"
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It's unclear what the price tag for the country would be, or whether Denmark would consider selling it.
Officials with Denmark's Royal House and the Danish embassy in Washington did not immediately respond to the Journal's request for comment on the talks.
The United States has previously tried to buy the strategically located country. President Harry S. Truman offered to purchase it for $100 million in 1946, but Denmark declined the offer, the Journal noted, adding the U.S. had also looked into acquiring the country back in 1867.
Technically a part of North America, Greenland is between the Atlantic and Arctic oceans, and between Canada and Europe. The U.S. has an airbase there, which is part of the country's state-of-the-art ballistic missile early warning system and satellite tracking system.
Dareh Gregorian is a politics reporter for NBC News.
Kristen Welker is a White House correspondent for NBC News.