The best thing that happened to Jamie was Brienne. She was the knight that he was once and she made him realize it. Respect begets Love. Not the other way around. I hope before one of them dies, they would be able to tell each other how much they love one another.
I have a feeling neither of them are going to make it out of season 8 alive but I really hope they have some time together before it happens. This song is so perfect for them.
Sadly I think there won't be much time for anything in season 8. I doubt any relationships outside of the Dany/Jon one will really be developed much, aside from maybe a reunion-esque thing between Gendry and Arya.
Oh don't get me wrong, I want it to happen so bad, I just don't think they will. If they do I think it will be an off hand comment / joke that a character will mention but I don't think they'll show it.