Despite Abrams's assertion that Luke is not Rey's father, this theory has always seemed like the strongest thanks to the film's heavy-handed hints that Rey is indeed connected to Luke in some way. One of the key moments comes during the scene at Maz Kanata's watering hole, when the lightsaber that belonged to Anakin and Luke Skywalker calls to Rey from the depths of the castle. After she touches it, she's instantly inundated with images from the past, and possibly the future, featuring Kylo Ren, Luke, Obi-Wan Kenobi, and Yoda. Is her connection to the weapon because it once belonged to her father? It's definitely possible, although nothing like that has really ever happened in the series before. Maz also tells her, “I have lived long enough to see the same eyes in different people. I see your eyes . . . I know your eyes!” Are they Luke's eyes, Maz? ARE THEY?!
The second big clue happens when villain Kylo Ren reads Rey's mind while she's being held as a prisoner of the First Order, and sees water and an island. After watching the movie, it's clear that was a direct reference to the island Luke has been hiding out on. The real question is whether or not that was a glimpse into Rey's future (which we see at the conclusion of the film), or a moment from her past, possibly suppressed, memories with Luke.
The third thing that really sticks out is Rey's intense Force sensitivity. With seemingly zero training, our heroine is able to push Kylo Ren out of her mind, expertly use Luke's lightsaber, and perform Jedi mind tricks on Daniel Craig. These are the kinds of things we've come to expect from experienced, highly trained Jedi, not people who've spent the entirety of their adult lives scavenging for scraps alone in the desert. Being a Skywalker would explain this.
Likelihood that Luke is Rey's father: ⭐️⭐️