Jon Snow may be dead on Game of Thrones, but that doesn't mean he can't come back. Although there are many theories on how that could be possible, my favorite is Melisandre uses her powers or "gift" from the Lord of Light to save or resurrect Jon Snow. Melisandre took an interest in Jon Snow from the moment she met him, and although Jon refused to be seduced because he was still clearly grieving Ygritte and didn't want to break his Night's Watch Vows, there was still some chemistry there. Plus, Melisandre quoting Ygritte's most memorable line, "You know nothing, Jon Snow," was equally creepy and curious. So could Melisandre and Jon Snow get together in Game of Thrones Season 6?
If Melisandre does bring Jon back to life, it wouldn't be that crazy for him to start developing feelings for her. When someone saves your life, that can make your feelings towards them completely change for the better. Plus, since Jon would've technically died, he'd be free from the Night's Watch and their vows. Jon would be free to hook up with anyone he so pleases, and why couldn't that be Melisandre?
After she killed Shireen and realized that Stannis would not win the fight for Winterfell, it made Melisandre question not only her beliefs but everything she's ever done. Melisandre probably won't be the same "Red Woman" we've known for the past five seasons. Shireen's death and Stannis' loss (and probable death) will change Melisandre. That's not to say she won't still be a priestess; she has to be to bring Jon back. But maybe now she won't be as ruthless. Killing Shireen was easy for Melisandre; doing something like that again would be a hard decision for Melisandre to make.
Now it seems Melisandre might actually have a conscience and that's something Jon could definitely fall for. Just like his father and his brother, Robb, Jon let's his heart lead him. He's honorable and caring to a fault, and Melisandre bringing Jon back and probably caring for him afterwards would definitely be something Jon like in a companion.
At this point I would just be happy if Jon Snow is alive. If he gets a new girlfriend on Game of Thrones, that'd just be a bonus.