She's 13, it shouldn't matter what her intentions are....
She's probably flirting with you. Or thinking she's flirting with you. I'd say that's pretty normal behavior of a girl her age. Most every girl has developed some sort of crush on an "older man"-- and at age 13 -- age 25 is an older man. Just relax, you aren't returning her affections.
It's more concerning that you haven't expressed your concerns to your wife. Talk to your wife about whatyou think is going on.