Disclaimer: I haven't read the books. However, I know that simply due to the nature of the first book being literature and not television, and thus having a lot more substance and material to back the world and characters, there's some solid speculation surrounding Jon Snow's bloodline.
It's a really hard topic because, to my knowledge, it's not like some super mystery that is fed across all the books. It's a theory primarily rooted, almost exclusively, in material dealt with in A Game of Thrones, the first novel. But the show didn't go into it as much, so it probably can't be discussed :/.
This sums up the current state of things very well between the book and the show regarding this issue.