We used to buy land.
What’s old could be new again, but liberal sensibilities prevent that.
So the only way we could get Greenland is if the people of Greenland wanted it, and I don’t see why they wouldn’t want US citizenship.
Greenland per capita income is $39,569 (as of 2015), which would make it one of the poorest areas if annexed. Only the territories would rank lower in income (although that almost $40k is double that of Puerto Rico, which is terribly low and declining). It also has just 56k population.