Zelda's been in a weird place in terms of characters for a while now. Ever since Melee, we have only ever gotten to play as different versions of Link and Zelda, as well as a scrapped F-Zero X character that was the original design for Black Shadow before the Ocarina of Time dev team decided to use that design for Ganondorf.
The other weird thing is that the unique movesets from the Zelda characters are Link, Zelda, and Sheik. The other half of the playable Zelda cast have been clones in one way or another.
I was also frankly surprised that we didn't get any new Zelda characters this time. It's a shame, as much as I like Link, Zelda, and not-Black Shadow, I'd really just like a Zelda newcomer that isn't one of those three.
If we're picking from characters that are not just popular with Zelda fans but at least video game fans in general, I think Skull Kid, Ghirahim, and Ganon have some of the biggest shots. Impa and Tingle MIGHT, but I dunno about them, given how consistently minor the former has been and how a whole country seems to dislike the latter. I like Impa, so it saddens me--maybe if Hyrule Warriors fans like her enough she could have a chance.
Skull Kid is minor in the grand scheme of things but he's still the most well-known character aside from Link in one of the most well-known and talked-about Zelda games of all time, Majora's Mask. Unfortunately, like Ghirahim, being an assist trophy in this game could hurt his chances. Lots of people might have seen the two of them and been like "Hey, they're here! Cool!" and have whatever desire for playable status for either of them fizzle out then and there.
I think, if any Zelda newcomer has a chance, it's gonna be someone like Skull Kid and Ghirahim (a memorable and significant character from a very memorable Zelda game--if not those two then a future character like them) or Ganon. We have had 3 versions of Link and 2 versions of Zelda, so Sakurai or someone else from Nintendo might include another form of Ganondorf, that being his Pig form. Unfortunately not even the King of Evil is spared from the "I dunno, maybe one day, I guess? Probably not through..." status.
Like with Skull Kid and Ghirahim, some people might be content with Ganondorf simply being playable and don't want another form. However this is at least offset by quite a few people's observation (they aren't necessarily Zelda fans--most video game players can tell this even without playing the Zelda games) that Ganondorf playing like an evil Captain Falcon doesn't seem quite right for him, and if another, more faithful form was available to play as, they might enjoy him enough to not mind the fact that there's two Ganons in the game. Still, there's ANOTHER obstacle for Pig Ganon to overcome--the form hasn't been in a new Zelda game that's been exceptionally popular. Pig Ganon is mostly known for the older games like A Link to the Past, and to a lesser extent Ocarina of Time (his human form was more popular there), so he'd be seen as a retro addition that isn't from NES and before, which Sakurai doesn't seem to enjoy that much. A Link Between Worlds doesn't really count, either, as he was just brought back so Yuga could possess him--he barely had any screentime. Sakurai and the Smash team like including characters that have been in video game players' consciousness around the time the Smash games are released, so Pig Ganon needs to be the main villain in a new Zelda game that's exceptionally popular for him to happen.
Disregarding ALL OF THAT, if any of those characters I listed were popular enough on the ballot, they might have a chance, too, lol. I was mostly talking as if we were debating the next possible Smash game (too soon, I know, heh).
Anyway, I hope this was an interesting enough set observations for this thread, haha. Carry on, fellow Smashers.