They seem quite intent on taking Greenland, as it's part of the empire's foreign policy strategy of dominating the Western Hemisphere and its resources in order to compete with China. This is all part of their new Monroe Doctrine 2.0, which they call the "Donroe Doctrine". They published this last year.

I think military action in Greenland is definitely a possibility in the event that the EU ends up refusing to negotiate. While Trump has refused to rule out using the military when asked about it, my guess is that they're hoping the EU will fold and make a deal to hand over the island before the tarrifs reach their maximum effect. Thess tariffs start at 10% in February, and then goes up to 25% in June, unless the US gets what it wants. It's a pressure tactic to let Europe stew in their own juices for a while. sicko-instapot

The ghouls in charge of EU foreign policy are rabid pro-US bootlickers who have no problem selling their own lungs to the US if it means saving the transatlantic relationship. The US regime knows this, so I imagine they're banking on this happening. If it doesn't, they always have their backup plan of just taking it by force. It's not like the EU can do much to stop them anyway.

But it will be interesting to see what the EU will do, because this will potentially have a huge effect on the future of both NATO and the EU. Making a deal with the US would not go over well with most Europeans, and member states aren't united on a response either. Depending on the outcome of this, it could do a lot of damage to the EU, and widen fractures that are already brewing in the background. Like France and Germany who don't see eye to eye on the EU's foreign policy, and see each other as a threat when it comes to being the dominant European power. seen-this-one

The Trump regime has also pretty much made it clear that they despise the EU now that they no longer need it, and actively promote fascist euroskeptic political parties in Europe that they probably hope to do business with after the EU collapses.