If Greenland is that important, we already have all of the money if we wanted to buy it, and all of the tanks and planes and nuclear submarines if we didn't want to take no for an answer.
Now THERE’S a price range!
For the cost of only $14 per American per year, we could pay everyone in Greenland $85k/yr for life. It’s $4.5/bln a year.
Greenland has already obtained some independence from Denmark and is looking for more. It’s unlikely they sell themselves to the USA directly but something that is effectively the same with a fig leaf on it could certainly happen.
And if actual world-scale conflict broke out, it would de facto be a US protectorate at best, and just another territorial acquisition at worst.
Economic incentives only go so far—there’s a cultural and political dynamic at play. If Greenland leans towards more autonomy, stronger US ties as a protectorate might happen naturally without needing to 'buy' anything outright. If they drift away from Denmark, North America becomes the obvious landing zone.