It may be a bit of a mutual love, since many Americans seemingly love Europe. They might see it as their ancestral homeland, or others might be fascinated by the history and culture. It's a popular destination for Americans to travel to.
Historically, the continents of North and South America have been fully Europeanized, as they were centuries ago. Every country in this hemisphere has, as its official language, a European language (mainly English, Spanish, French, Portuguese, and a few Dutch colonies which remained). Their governments and political systems were formed from the European colonial governments from which they sprang. Even the continent itself, "America," is named after a European navigator and mapmaker.
In many ways, one could say that America is an extension or outgrowth of Europe, even if separated by 3000 miles of ocean. So, if Europe becomes "Americanized," then it's process referring to a country which has already been "Europeanized" and continues to be so.
If the whole world became Americanized, we could all become Americans - one big happy family.