That would require the (politically unlikely) agreement of the Danish government. See article 2 of the relevant treaty [1]:
"...establishing and/or operating such defense areas as the two Governments, on the basis of NATO defense plans, may from time to time agree to be necessary..."
> The only reason Trump wants Greenland is he's not all there -- Greenland looks big on the map so he's fixated on it.
I agree that that is part of it, but there is more to it than that.
(I'm not Danish or Greenlandic, so this is just my reading of the situation.)