When I was a child, I loved reading, but my older brother – who grew up in the same environment – would barely touch a book. As a teenager he got into reading because he found a genre/topic that interested him (in his case then, it was sci-fi), but before that it was like pulling teeth.
You might want to ask your youth services librarian for book recommendations for books that you think might be of interest to her – they know their stuff and might have something good up their sleeve so that she can get into reading at a younger age than my brother did!

Hard as it may be for a book-lover to understand and accept, there are people in this world who do not like reading! However, reading is a necessary skill for a child and one should persevere for a few years at least. Maybe you can try different kind of books? You may be surprised at what piques her interest.