I do think that DQXI's potential platforms are an interesting discussion for a number reasons, so I thought I'd try to analyze all the potential platforms.
First, I'd like to narrow down what we know and the potential timeframe since it changes the viability of certain platforms present and future.
What we know:
1.) Historically speaking, Dragon Quest has been on the best selling platform around the time of its release (excepting for brand new platforms with no install base). It used to be on a single platform, though it has become increasingly multiplatform between the ports to PS1/PS2/DS/3DS/Wii and (almost the entire series) to mobile. Dragon Quest X is now also on five platforms between Wii, Wii U, PC, mobile, and 3DS (the last two are cloud streams of the PC version). Toward this end, one of Square Enix's staffers on the series noted that since users are more spread out these days, it's important to incorporate more platforms to reach them. It's not 100% clear if he was just referring to DQX or the series on a go-forward basis, but they have been following through with at least DQX quite heavily.
2.) Yuji Horii directly implied that DQXI isn't a mobile game. Well, it might be 2-3 years after launch, but what's important is that it's not being designed or launched at one, so it's presumably a full priced retail title as opposed to an f2p service.
3.) Horii noted that the game was progressing toward a calendar 2016 release for DQ's 30th anniversary. It's unlikely to be out before April 2016 (start of fiscal year 2017) for reasons I will detail soon.
4.) Yuji Horii noted he would like to play it on a big screen. For the purposes of this discussion, let's take him at face value and assume he means it will launch on at least one platform that can output to a TV, be it a console or a handheld with TV out.
5.) For the last few entries, Square Enix has released a bunch of Dragon Quest spin-offs and/or ports on the game's main platform prior to releasing the main game. So far the only platforms that have gotten that treatment are the 3DS and mobile, of which the latter has been largely ruled out for an initial release.
Explanation of why I feel we can limit it to April 2016 or later instead of just calendar 2016:
Square Enix has noted that they want to grow revenue and profit each fiscal year for at least the next five fiscal years. Currently, Tomb Raider is the only confirmed title for fiscal year 2016 (April 2015 - March 2016). Tomb Raider, at 6.5 million copies, was actually Square Enix's best selling retail game last generation (Final Fantasy XIII was only 6.3 million as of our last update). Square Enix has stated they plan to unveil Triad Wars, Hitman, and Deus Ex in 2014. Just Cause 3 was also explicitly listed on a resume as releasing in 2015. It's likely that at least two of those will make it out next fiscal year, and could be significant (2-4 million) sellers based on the previous entries. Even if we assume that Final Fantasy XV won't release until April 2016 or later (a fair assumption), this is still a very hard hill to climb in Fiscal 2017 (April 2016-March 2017), so putting Dragon Quest XI out before April 2016 would make it basically impossible to achieve their stated financial goals.
And now, on to the potential platforms:
1.) 3DS: I feel given the five starting criteria, this is pretty much a given. Square Enix has put out a ton of Dragon Quest games on the platform, they've ruled out mobile as the platform for DQXI, and the 3DS will still be the platform with by far the largest active user base as of 2016. Given a mainline retail Dragon Quest game will want to sell 3-4+ million copies, I don't think it's feasible to not release on 3DS. Co-op has also become a central part of the series over the last two entries, and the 3DS's userbase size and local/online multiplayer capabilities both fit this very well. Dragon Quest also doesn't shy away from releasing very late in a platform's lifecycle.
2.) 4DS: Obviously, with a 2016 release, the question becomes if Nintendo's next handheld will be out by then. While I certainly think they should release in Q4 2015/Q1 2016, I'm not strongly confident they will. That said, if they do, we do have a precedent with DQX (and frankly the entire industry at this point) for doing a cross-generational game between 3DS and 4DS. Any asset upgrades done for this would also work will with any potential console ports, since 3DS graphics are a bit rough even for Japan's standards for a straight port to home consoles. Something like the upgrades for Resident Evil: Revelations should be sufficient given what sells at retail, and not overly expensive to do. There's also a potential here since both the 3DS and 4DS are Nintendo platforms to let 3DS and 4DS copies play local multiplayer together instead of splitting up the local multiplayer handheld userbase.
3.) Wii U: Well, 2016 is pretty late, but the Wii U should have at least some kind of installed base at that point. If the system climbs to 3-4 million by then, even though some of the active userbase will have left, I don't think selling 400-500K on the platform is off the table. If a commanding requirement of the project is having it on at least one TV capable platform, this is not a bad choice.
4.) PS3: Well, Q2 2016 or later is a pretty rough time to be releasing a PS3 game honestly. The system is selling in a 7000-9000 unit range already and Q2 2016 is almost two years from now. It's true that the Wii U and PS4 are also selling in this range, but the PS3's support is on its last legs whereas the PS4 and Wii U are at least going to be getting some software support in 2015-2016. While totally feasibly from a technical perspective, I don't see it as being a viable platform from a business perspective unless DQXI is going to be on literally any platform that has a potential userbase to sell to.
5.) PS4: I find this more feasible than the PS3 since by 2016, if the PS3 audience is going to move to the PS4, a lot of the active buyers should have moved over by then. The question becomes "Is there a notable audience that will own the PS4 and buy DQXI on PS4 that won't own or buy the game on 3DS and whatever other platforms it's on?" If the answer is yes, then a port is obvious. If the answer is no, the question shifts to "Are we going to put it on PS4 anyway to send a message that we're a majorly multiplatform series going forward?" For example, Square Enix has Type-0 HD on Xbox One, and has been clear in interviews that they are still trying to convince Microsoft to let them release FFXIV on Xbox One. With Final Fantasy, Square Enix is trying to send the message that "If it's on PS4, you can also play it on Xbox One and don't have to worry about missing games." Now, for a series that has 50-60%+ of its sales in the West, this is a braindead obvious move to make. This is decidedly less clear for Dragon Quest, a series that they only seem to be localizing on mobile anymore. If they want a platform that will still be relevant in the West in 2016, the PS4 is a good choice, though it will have the presumably rough graphics going against it. If they only view the title as a niche ~200K unit series that they might not even localize, the potential audience for the game will likely have a 3DS anyway. I think this is a platform that's on the table, but less likely than the Wii U or 4DS.
6.) XB1: The only way this game is on Xbox One is if they decide they're making a major Western push and putting it on every platform that's popular in the West.
7.) PC: See Xbox One. If it's a 3DS game there's no need to make a PC version to use for cloud streaming, and if it's a retail game instead of an MMO or f2p title, it's not a great candidate to extend into mainland Asia.
8.) Vita: I left this one until now since I think it's an interesting option to discuss, but also probably the most controversial. With the Vita, we're frankly looking at a system that's likely to be the last PlayStation handheld, especially anything beyond a device that streams PlayStation Now or whatever. Putting the game on Vita doesn't build you an audience you can capitalize on with the Vita 2. It's also a handheld, and one that's definitely not going to be able to play local multiplayer with the 3DS version. With home consoles, people can at least find other people to play with online and have to be in their house anyway. If they have the Vita version of a co-op game, and some kids they meet on the train or the after school study center have the 3DS version, they get left out. Since this a product line with a ticking death clock, Sony is also much more likely to be interested in convincing them to get the game on PS4 if they can only convince them to add one platform. Q2 2016 or alter is also a really long time from now, and even though the Vita's health has improved, I'm unsure how much life it has left in it. Once developers start getting ready for the 4DS or adopt the PS4, along with the continuing flight to mobile, this lowers the potential Vita developer base (barring Vita/4DS or Vita/mobile cross-platform games) as time goes on. On top of all of this, the Vita's biggest hits haven't sold all that much, especially in terms of what a Dragon Quest games sell. Overall, like the PS3, I don't see this happening unless the goal is to get it on as many platforms as humanly possible.
9.) Wii 3: I don't feel comfortable enough on determining when this is releasing to really speak to it with much accuracy. I will note that Nintendo has implied that they're going to make it much easier to move 4DS games to Wii 3 and vice-versa (perhaps to the point they both run an iOS/Android like OS that makes what's literally the same game run on both platforms), so if there's a 4DS version, there's obviously a potential there. Will the platform be out in a time frame that makes it relevant to the discussion? I don't know.
10.) 360/Wii: These are dead platforms.
11.) iOS/Android: These were largely ruled out for an initial release, but I do want to note they're almost assuredly coming 2-3 years or so down the road in case anyone skipped the other parts of the post. See the entire series getting ported to mobile sans DQIX for an explanation of why.