When Daenerys is in the House of the Undying, she hears a prophecy that states "the dragon has three heads." This is widely assumed to mean the "three heads" are the three riders meant to fly on Drogon, Viserion, and Rhaegal, and those riders are thought to be Dany (for obvious reasons), Jon Snow (because his parents are rumored to be Lyanna Stark and Rhaegar Targaryen), and Tyrion. All three of their mothers died in childbirth (assuming you buy into the "Lyanna is Jon Snow's mother" theory), and we'd be very, very surprised if such a strong connection like that ended up being merely a coincidence.
