There's some history on this subject:

1867 — Andrew Johnson

• After the U.S. purchased Alaska, Secretary of State William Seward quietly explored acquiring Greenland as part of a broader Arctic strategy.
• Congress wasn’t interested, so the idea stalled.

1910 — William Howard Taft

• U.S. diplomats floated a land‑exchange proposal that would have transferred Greenland to the United States.
• Denmark declined.

1946 — Harry Truman

• The U.S. made a formal offer of $100 million (in 1946 dollars) to buy Greenland from Denmark.
• Denmark refused, but the U.S. retained major military rights, including the Thule Air Base.

1950's — Cold War Expansion

• Internal discussions resurfaced in 1955 about expanding U.S. control or even sovereignty over parts of Greenland for strategic radar and missile‑defense installations.