According to
this site, the quote is attributed to Elbert Hubbard (who is an author).
As for the quote? I guess it's a matter of how you define "enemy" and what that entails. If by "enemy" you mean someone that you know that you just don't get along with and choose to avoid, then I'd say the quote might be true.
However, if an "enemy" is someone you actively disagree with and "fight," then the quote is not true at all. You don't have to actively engage against an person in order to actively engage in a relationship with a friend. That's silly.