Trump's MO is to bluff other countries into compromising on a deal to his liking, in this case to further our national security interests in Greenland without necessarily owning the place. I do not believe there is any other country on Earth that could gain control over Greenland, nobody else has the means if not the balls. Cuz that would be unacceptable to the US, Canada, and NATO and could lead to WWIII. I ain't seeing that as likely.
I think Trump wants some concessions from Greenland/Demark, maybe another base of some sort. Maybe he wants dibs on Greenland's natural resources that has little to do with national security. I'm pretty sure he would need congressional approval to annex Greenland in some way, and frankly I do not see the democrats supporting that action even if it is our best interests to do so. Politics don't you know.