J.K. Rowling said this, "A very famous writer once said, 'A book is like a mirror. If a fool looks in, you can't expect a genius to look out,'" on NBC's 'Today Show' on Oct 20, 2000. Who is the famous writer she was referring to?

Searching Google for the term "A book is like a mirror" yielded quotes similar to the one you have from both Martin Luther and Georg Christoph Lichtenberg (as both would be writing in German, Rowling's quote would have been translated in either case and wouldn't match word for word).

I'm not sure how to decide between the two, but the source I would consider to be most authoritative (The Columbia World of Quotations) gives Lichtenberg as the speaker of "A book is a mirror: if an ape looks into it an apostle is hardly likely to look out"

The Columbia source is at: http://www.bartleby.com/66/1/36001.html

"Books are like a mirror. If an ass looks in, you can't expect an angel to look out."


Arthur Schopenhauer, Parerga and Paralipomena


http://www.famous-quotes.com/?page_id=10280

I think the reference to Schopenhauer on the site may be a misattribution.

The quote doesn't show up when searching for "mirror" in either volume of the translation of Parerga and Paralipomena on amazon.com. On the other hand, it appear on page 71 of "The Waste Books" at
https://www.amazon.com/Waste-Books-York-Review-Classics/dp/0940322501/ref=pd_bbs_sr_1/104-7902609-4302363?ie=UTF8&s=books&qid=1180112193&sr=8-1