Y'know what, this is the juiciest bone speculation has gotten in ages, so I'm going to waste a bit of time on this. Assuming these are deliberate clues, here's our current criteria: character has psychic powers or otherwise has a vision, and there should be some connection to the number 3. I'm going to do a quick survey of the characters in
the comments of the stream announcement's Smashboards article as well as top threads here in Newcomer Speculation and see if any of them fit the bill.
First, here's a bunch of notable characters that I don't think fit those clues, in no particular order: Dante, Steve, KOS-MOS, Elma, Travis, Geno, Doomguy, Ryu Hayabusa, Crash, Shantae, Agumon, Andy, Sora, Professor Layton, Dixie Kong, Bandana Dee, Reimu
Here's the weird part: I don't think anyone fits those two clues very well, so I don't have a strong prediction for tomorrow. Still, here are the ones I think fit the best:
Byleth - Three Houses is one of the more obvious "3" connections. As for the psychic angle, one of the plot points is their "revelation", which is close enough in my book. A Nintendo character doesn't really fit the third party theme we've had throughout the Fighters Pass, but I think Byleth remains plausible.
Isaac - One of the few characters that has a clear-cut psychic connection with Psynergy, at least in terms of powers like telepathy, mind-reading, etc. "3" is a stretch, but you could go with angles like three games or missing out on 3 Smash games. I admit this may be me seeing what I want to see, and like Byleth he fails the third party test, but I think Isaac works well enough to consider.
Master Chief - It's probably foolish to follow the "Oracle" translation closely, but that's an important term in the Halo universe. I'd also argue the original Halo trilogy is by far the most famous part of that franchise, so there's a semi-plausible 3 there. Perhaps more importantly, he's an extremely famous video game figure from a third party that already has a character in the Fighters Pass. I think he's worth considering.
Phoenix Wright - Maya and the Fey clan are all spirit mediums, which fits the psychic mold well enough, and there's little doubt the original trilogy is the most famous part of the Phoenix Wright series. Both are admittedly stretches, but he's one of the few characters I can fit to both clues with relative ease, and he's a third party like the rest of the Fighters Pass, so that makes him plausible to me.
That's all I've got right this second. If I had to guess among those four, I think it's going to be Phoenix Wright, but really all this exercise has convinced me of is that I'm going to be surprised one way or another. Tune in tomorrow when I'm completely wrong about all of this.