Any familial ties between Rey and other characters have yet to be confirmed.
J.J. Abrams did release an answer to a young fan back in April of 2016, stating:
"Rey's parents aren't in Episode VII. So I can't say in this moment who they are. But I will say it is something that Rey thinks about."
J.J. Abrams later restated this remark later on:
"What I meant was that she doesn't discover them in Episode VII. Not that they may not already be in her world."
I always took this statement as Rey's parents aren't discovered in Episode VII, so it is up for debate if they are or aren't.
J.J. Abrams is not directing Episode VIII, Rian Johnson is. J.J. Abrams has also released statements expressing his wishes to respect and value the secrecy to the film:
"Obviously it is not for me to talk about in this moment because this is Rian's story to continue now. The last thing I'm going to do is reveal something that he would be upset about. I want to make sure that Rian gets the courtesy he showed me."
Daisy Ridley also stated she knows who Rey's parents are, but that it is the journey of the character, rather than her parentage that is important.
Episode 9 director, Colin Trevorrow hinted that Rey's parentage might not be discovered until Episode 9. But he has stated that Rey's father is someone that we have met before in the Star Wars universe.
"We're going to make sure that the answer is deeply and profoundly satisfying. Rey is a character that is important in this universe, not just in the context of TFA, but in the entire galaxy. She deserves it. We'll make sure that the answer is something that feels like it happened a long time ago, far away, and we're just telling you what happened."
Colin Trevorrow went on to state that Luke and Leia would have more prominent roles in Episode 9, and that he's excited to find "new places to take these characters."
Ian McCaig, who was a former artistic director of Lucasfilm and worked on previous films' storyboards and concept art, gave teasers concerning Rey's parentage. He stated in early drafts of the TFA, there was going to be a romantic teaser between Qui-Gon Jinn and Shmi Skywalker. This was scraped as they did not want any material from the prequels. Despite Disney's insistence, some of these concepts remain throughout the Star Wars universe. McCaig ended his statement with:
"and now we have a new Skywalker."
In short, Disney and Lucasfilm are teasing who Rey's parents are but we are going to have to wait for the whole trilogy to wrap up in order to find out. Speculations and theories are fun and enjoyable, but at the end of the day, we are left with no real, solid answer. We'll know who Rey's parents are..in time. But it doesn't seem like any real confirmations or answers are going to be let out any time soon.
Caution: spoilers ahead for The Last Jedi (this includes the links below):
In The Last Jedi, Rey's parents are revealed to be:
random people who were junk dealers who sold and abandoned their child. They are currently dead; buried on Jakku
However, in an interview with Rian Johnson, he has also stated that the answer provided in The Last Jedi is still up for debate until Episode IX:
I can’t speak to what they’re going to do. And there’s always, in these movies, a question of ‘a certain point of view.' But for me, in that moment, Kylo believes it’s the truth. I don’t think he’s purely playing chess. I think that’s what he saw when they touched fingers and that’s what he believes. And when he tells her that in that moment, she believes it.
In another interview with Huffington Post Rian Johnson further discussed why Rey's parentage is still open for debate:
Anything’s still open, and I’m not writing the next film. [J.J. Abrams and Chris Terrio] are doing it. With all of these movies, Obi-Wan’s whole speech about a certain point of view always applies, so I think that you have to always think about the context of how information is given. But for me, dramatically, that’s why that reveal at that moment made sense.
So it still appears that we'll have to wait for Episode IX to solidly confirm The Last Jedi's parentage claims for Rey.