Late to this discussion, but I'm going to contribute anyway considering I'm an expert within the whole "FFXVI speculation" niche.
Naoki Yoshida has already confirmed that as long as FFXIV is in operation, he can't leave it. He views it as his baby and even if he's hands-off during actual development, he will always be routinely consulted about the game. Therefore, he'll always be involved.
http://uk.ign.com/articles/2015/06/05/meet-the-man-who-redeemed-final-fantasy?page=2
Considering they plan to have FFXIV have a 10 year life-cycle, he's stuck on the game until at least 2020 (if they go off the release of the original FFXIV) or 2023 (release of ARR). Therefore, no. There's no chance Naoki Yoshida will helm FFXVI. It's more likely that he'll helm FFXVIII and it will be another MMO. As it stands, he the only competent MMO director at SQEX, and considering the huge success of ARR, I don't see SQEX management or MMO Final Fantasy fans wanting him taken out of that genre for his next game.
With that cleared up, I'll return the subject of FFXVI to the most likely candidate: Hiroyuki Ito.
It has finally come to my attention (a few weeks ago, actually), that Hiroyuki Ito is in Business Division 5 (BD5). My source in a high ranking employee at Square Enix Japan who confirmed this to me over on Twitter. I won't say who, as I think this info was supposed to be classified, as they have since deleted the tweet. I don't want them getting in trouble for revealing this, so I will not name drop them. Anyway, that info finally put my investigation on Hiroyuki Ito's location to rest. However, more question arose with this info. If Hiroyuki Ito is indeed in BD5, why didn't he work on FFXIV (both ARR and Heavensward)? He's not even credited in the "Special Thanks" section for both. Furthermore, it would appear that many FFXII staff that worked on ARR, didn't work on Heavensward. The FFXII staff headcount on Heavensward was massively reduced from ARR. Ridiculously so. The thing is, some were still credited under "Special Thanks" on Heavensward, meaning they're still within BD5.
People need to remember that both The Last Remnant and Tactics Ogre PSP teams (and therefore the majority of the FFXII team) were merged with the original FFXIV 1.0 team back when the team was restructured to make ARR in November 2010. It would seem that now, with ARR released, that huge, bloated team was massively reduced. Heavensward has only 20-25% of the headcount ARR had. All those staff that have left (many of them FFXII staff) must have moved on to another project. If Hiroyuki Ito's really within BD5, it would seem the staff have been given to him and his project has finally begun to ramp up.
The stars are lining up.
If Hiroyuki Ito is indeed within BD5 and not working on FFXIV in any capacity, there must be another team within BD5 that has him at the helm. Yoshinori Kitase told me back in February 2014 at the LRFFXIII European launch event, Ito has his own team at SQEX Japan and planning his own project. In that same month, he told Eurogamer in an interview that FFXII HD happening depends on if the FFXII team (and therefore Ito) wants to make it. Earlier this month, Arnie Roth let it slip that a FFXII HD is now in the works. It would appear that within BD5, the FFXII team has reformed. This means that both the FFXIV team and FFXII team exist within BD5. I have not idea how big this division is, but considering that BD1 through to BD4 were once unified as the 1st Production Department, the size of BD5 could be really big, especially seeing as it houses the original FFXIV, The Last Remnant, and Tactics Ogre PSP teams.
It's also worth noting that Naoki Yoshida already hinted that after he's done with FFXIV, he'd love to make a game completely in secret and tell nobody about it. Instead, he'd develop it up to a point where it's about to go gold, then suddenly reveal it to the world.
I find this statement interesting, as considering how long Hiroyuki Ito has been MIA, this could be the development philosophy he's following with FFXVI. It's also worth noting that FFIX, which Ito directed, was publicly announced only a few months before it was released. FFIX was announced in January 2000 and then released in July 2000. Ito might be following the same philosophy with FFXVI.
Also, Naoki Yoshida said he doesn't believe FFXV will restore FF to the greatness it once had. He personally doesn't believe FF will achieve this feat until FFXVI or later.
Considering FFXVI could be in development within the same Business Division as his own FF game, he's obviously seen it and knows aspects about it that the public don't. The game could be considerably more grand and ambitious than FFXV, which is why Yoshida has the confidence to make such a strong statement that demeans FFXV, which many people feel is the most ambitious FF game to date. With Hiroyuki Ito at the helm of FFXVI, there's no way it would not be ambitious. The man has already gone on record to say that last-gen (PS3/Xbox 360) couldn't handle his gameplay ideas.
If Hiroyuki Ito gets his way, we'll possibly see FFXVI announced very close to it going gold. That would be a welcome change of promotional strategy, especially after the whole "FFXV releasing 10 years after it was announced" fiasco. The downside? Don't expect FFXVI announced until 2019.
Honestly, the wait for Ito's next FF is tiring. People like
@Sora96 may be stressed out over not knowing about Motomu Toriyama's next game, but his last game only released last year. Hiroyuki Ito fans been waiting on this man since 2007. That's the last time he dropped something new or even contributed significantly to a game. If FFXVI is a 2019 release, that's 12 years after FFXII IZJS for another new game with Ito as director. That's the same amount of time James Cameron took between Titanic and Avatar! Why do these two incredible directors take forever in their respective mediums? That's what happens when you're an ambitious creator, I guess. FFXVI better be as groundbreaking as Avatar was when it finally drops. That said, with Hiroyuki Ito at helm, I already know that it will be.