Still going to say the easiest explanation is that she was the child of one (or two) of Luke’s students and they hastily left her on Jakku while on the run from the Knights of Ren.
Perhaps the child of one of Luke’s students and Luke. After all, his mother robbed the cradle. And his father abandoned his children. 
Watched the movie again last night. She clearly says she is waiting for her ‘family’ to come back. Not mother, not father, ‘family’.
It will be interesting to see what they do with her parentage. They’ve left it just ambiguous enough that any of these speculations could turn out to be correct. One of us will get to crow that we were right all along. 
Pretty sure jj said that rey isn’t related to anyone in force awakens so that puts luke and the solos out.
Did JJ then add that her father was just some guy named John Harrison?
Maybe Shmi popped out another Parthogenetic spawn between Qui Gon and Clieg and pawned that one off on another Passing Jedi, to be raised anonymously on a random Desert planet, who then got forgotten in the chaos of order 66, and had a child of it own and simply continued the Skywalker genetic programming of abandoning children on desert planets for a couple generations until the Force Awakens.
Hmm. Don’t remember that. Cite?