>>32652571Red in the manga, the original arc had like a harem thing. Classic shonen stuff.
It's implied offscreen that his friendship with Blue strengthened since he didn't trust her at all cause they had a Batman and Catwoman thing going on.
Then in GSC, it's basically concrete that they're really close friends.
Then in FRLG, it sheds light from Blue's perspective of how much she's changed because of her friends and it's heavily implied that Red is the one who helped her change into a better person as she started to nickname her Pokemon. (Green doesn't nickname his Pokemon, Yellow doesn't get her Pokedex until the end of FRLG)
Also in FRLG, Red and Green both try to get stronger to avenge Blue as she's traumatized into a very very short coma when she witnesses losing her parents, and when Red kinda falters, she's the one to try and cheer him up even though she's injured + still dealing with that emotional trauma of losing her parents to Deoxys.
In ORAS, the two still hang out and Red specifically calls for her assistance since his BFF Green is in Kalos (XY arc?).
So they're like really good friends. Unsure if you want to take it as romantic, it's more natural than seeing Yellow being all flutter blushy and all the fan-art that comes associated with that where they portray him as a dumbass even though the manga directly shows that he's not that clueless as like for example, Ash.
Manga hints heavily that he's had an affection for Blue (because she's cute), and he's had a crush on Misty and trusts her a lot for advice and other things as she's the one who helped take the Team Rocket threat seriously since he didn't really give a fuck before. But he avoided all that romance shit at the end of GSC since it was on the spot, and there was like 4-5 other people around eavesdropping.