I recently read a forum post online claiming that Melania Trump is a Slovenian citizen. However, I haven't heard anything about this in the news and couldn't find information online.
It is common knowledge that she was born in Slovenia. According to this article, she immigrated to the USA in 1995 or 1996. According to RefWorld, people who were Slovenian-Yugoslav citizens and residents of Slovenia upon independence in 1990 acquired Slovenian citizenship automatically. As I understand it, she lived there at this time.
As she doesn't seem to have automatically lost citizenship under the clauses that automatically revoke citizenship, she likely would have needed to renounce it to not be a citizen(assuming that she did indeed acquire that citizenship in the first place).
I have, however, found no credible discussion of whether or not she has renounced her Slovenian citizenship. It does seem odd to me, however, that it hasn't come up in an interview if she maintains her citizenship.