The Danes did offer to sell Greenland to the United States in the late 1800s. The U.S. balked doing so (in large part because the media and congress criticized the purchase), but instead we offered to buy the Virgin Islands. That deal got finalized in 1916 and the purchase price was $25 million. Too bad we did not pay a bit more and get Greenland then too.
I doubt the Danes want to sell Greenland now, but just like in World War II was about keeping the Nazis out, and the cold war was about keeping the Russians out, the U.S. wants to make sure hostile forces (like the Chinese) don't come in the top of North America. Danes are welcome, but Chinese entities who just want to "help" are not.
The Alaska Purchase was criticized, till gold and later oil was discovered there. Wise move to have gotten the Russians from abandoning their North American foothold.
Rush Limbaugh: Understanding Trump and Trump promises not to do this to Greenland
A View From The Beach: The Girls of Greenland
Greenland cold-sholders purchase offer
I promise not to do this to Greenland! pic.twitter.com/03DdyVU6HA— Donald J. Trump (@realDonaldTrump) August 20, 2019