Basically, yes, and no, respectively.
By all reports, he asked quite a few people in his administration during his trip if the US could buy Greenland many times - not just once, but repeatedly. And answers ranged from "Hahahahaha, that's quite the ridiculous remark, sir!" to "Actually, you never know - let me contact a Danish official and see what we get. [Two hours later] Danish official says no."
Unfortunately, while this is clearly an exhibition of insane thinking, the BBC has pointed out - and I'll never forgive the BBC for this - that there are two precedents in history for such a line of inquiry; both Andrew Jackson and Harry Truman made serious offers to Denmark for Greenland that didn't go anywhere. So while this is definitely a symptom of Trump having no go***mned mind at all, it can be argued that this is merely an extension of an inquiry that the United States has already made in the past.