
If it were 彼女の話, it would match.
I'm not quite sure what this sentence means with に, or whether it even is correct.

Here the に marks an indirect object.
Let's ask (聞きこう, finite verb) to her (彼女に, indirect object) her story (話を, direct object)

I'd phrase it as 「聞いてみよう」 in that case. Depends on the context, of course.