Harry Truman thought it was a good idea too:
That's why, according to the AP's account of the National Archives papers, Truman's advisers prized the geographic advantage Greenland could afford to defend against Soviet strategic bombers that might fly over the Arctic Circle toward targets in North America.
The United States opened negotiations with Denmark about using Greenland, and at one point, the American side proposed buying the island outright for $100 million in gold and the rights to a patch of Alaskan oil.
All this took place in confidence but even then " as now " the idea shocked the Danes. Here's how the AP's W. Dale Nelson described the National Archive documents' account of the exchange:
Secretary of State James Byrnes made the offer to visiting Danish Foreign Minister Gustav Rasmussen in New York on Dec. 14, 1946, according to a telegram from Byrnes to the U.S. Legation in Copenhagen.
After discussing other security arrangements for Greenland, Byrnes said he told Rasmussen that perhaps an outright sale to the United States would be the most clean-cut and satisfactory.
Our needs ... seemed to come as a shock to Rasmussen, but he did not reject my suggestions flatly and said that he would study a memorandum which I gave him, he said."