The Danish are not interested in selling it, nor does it seem that Greenlanders are interested in declaring independence and then voting to join the US. (IIRC such a move was polling somewhere in the single digits.) A military takeover would go over poorly. Even if it went swimmingly, it would backfire, as an on-the-fence Europe would break from the US orbit, end or reorganize NATO, and establish much closer trade relations with China -- the latter move is already being pushed in certain quarters, on the grounds that it's growing increasingly necessary for the EU's economy.

Somehow I doubt it. Trump talks a lot of stuff that he hasn't been able to do, like lowering prices on food and gas.