Square Enix's Third Development Division is working on something big, and it could very well be Final Fantasy 16, but division head Naoki "Yoshi-P" Yoshida doesn't want us to get it twisted. Whatever that project is, and whether or not it is Final Fantasy 16, Yoshida will continue to focus Final Fantasy 14 for the foreseeable future.
RPG Site reports that during a recent official stream for Final Fantasy 14, Yoshida took a moment to shoot down rumors that he's the director of what will be revealed as Final Fantasy. "I'll say it clearly—it's annoying[...] I'm still going to continue being in charge of FF14 for more years to come (as long as I don't die from sickness or accident)," Yoshida says. "So please ignore any non-official announcements. It's so bothersome."
One might think that since Yoshida righted the ship with Final Fantasy 14's A Realm Reborn way back in 2013, having him hop over to a new title as a director might be long overdue. On the other hand, even since becoming head of the Third Development Division last year, Yoshida's been extremely active and involved in Final Fantasy 14's development and community.
While it's possible Yoshida could be pulling double directorial duties, it could also be the case that he's actually taking a more hands-off role in whatever the Third Development Division's next-gen project is. As of last November, Square Enix announced that the new title had "completed environment development and is now moving into a full-scale large-scale development phase." In the meantime, we know Yoshida's been busy with post-Shadowbringers updates and continuing Final Fantasy 14's string of crossover events.
For now, it seems quite reasonable to take Yoshida at his word and trust that when he says he's working on Final Fantasy 14 for years to come, he means it. Final Fantasy 16, or whatever secret project Yoshida's division is working on, could easily be a chance for another Square Enix developer to make their own mark as a public-facing game director.
If, on the other hand, we find out the project is Final Fantasy 16 with Yoshida as its director, then you've got to wonder where he could possibly find the time. If anyone could steward an MMO into a new decade, make a call to collaborate with Blizzard, lead a next-gen title and rack up a cameo in Nioh 2 all at once, it's Yoshi-P.