If my fuzzy memories are anywhere close to correct, Trump wanted to buy it in 2017, Denmark said no, and he went on to slapping stupid[0] tariffs on Canadian and European exports before putting tariffs on China.
Trump's 2025 playbook seems entirely identical. The thing is, America has wanted Greenland for at least a century[1]. I would not be surprised if there's some long-timer in the Executive Branch that just happens to have a chip on their shoulder about how much America should have a Greenland. There's a lot of reasons why America would be safer and wealthier with the island, but Denmark isn't going to sell it. Hell, Greenland itself doesn't even want to be Danish, much less American[2].
[0] They're stupid because any hope of America remaining economically prosperous without China to sell us cheap shit (or Saudi Arabia to sell us cheap oil) relies on having a large free-trade area. Y'know, the sort of thing TPP was supposed to give us.
[1] https://en.wikipedia.org/wiki/Proposals_for_the_United_State...
[2] https://en.wikipedia.org/wiki/Greenlandic_independence