I think this may have been part of an anthology, as it seems like the story was short. I used to read anthologies like "Sword and Sorceress", so it may have been in something like that.
What I remember: There was a library that was renowned for having a great many books. You couldn't take any books out, only read them there, and the Librarian always knew exactly where every book was. I think it was being told from the POV of a young woman who was talking to someone else who suspected that the Librarian was a dragon and this was their hoard. He took her into a side room with a book to prove his theory, and very shortly after the Librarian came to find them, knowing exactly where they were since they had a book.
When I read it: Sometime between 1997 and 2008.
Book description: I don't remember anything about the book itself, just the story. I don't know if it was hardcover or paperback, or any cover art or anything.