Saying Rey is an offspring of any of the three characters is problematic. Leia/Han would have recognized her if they had a daughter (though Han may have forgotten, Leia wouldn't have). If you think it's Luke, then the immediate question is "who was Mom?" because immaculate force conception would work only on, well, a woman.
But the above kind of flies in the face of destiny trying really hard to get Rey to accept Anakin's lightsaber. For that kind of setup one would figure that she's part of the Skywalker legacy... or is she? One theme of this trilogy could be that greatness is not passed on by blood. Kylo is hellbent on assuming the mantle of his grandfather, but our protagonists are standing in his way.
it could be Mara Jade. in the scene where Rey finds Luke, there appears to be a grave marker that Luke is standing next to. could it be of his deceased wife? If Mara (a powerful Force user) was indeed Rey's mother, this could explain Rey's natural strength in the Force and why she was able to resist Ren's interrogation with no training. this is, of course, just theory and speculation.
Mara is one again canon because Disney has reprinted the Thrawn trilogy with the Disney logo on the backs of the books. I am fearful of my theory because that would mean Mara is dead, but is established to be a character in the movies.
Edited by Jester006