I do not approve of empires. I don't approve of Denmark having land in/near North America. I do not approve of the US having land elsewhere - we made the right decision with the Philippians to make them an independent country after winning it. (Guam makes sense as a US navy base, but otherwise should be an independent country, there are a few other islands in the area that US has that don't have the population to be independent, but I support turning them over to New Zealand/Australia)
That said, Canada is the obvious owner for Greenland if they can't be an independent country, not the US.