http://www.siliconera.com/2014/06/12/dragon-quest-xi-development-will-made-home-consoles/
Well according to this it's made for home consoles, so that rules out 3DS and mobile. Seems risky to me not putting it on 3DS.
Besides this, we have Wii U, NX, Xbox One, PS3, PS4. We can rule out the XBO for obvious reasons. I doubt at this point in time they'd release it just for PS3. This leaves us at Wii U, NX, PS4, and PS3/PS4.
Some people think Wii U might be easy to rule out, especially if the NX comes out in 2016, but we have no idea when this started development. When it started development they might have had no idea about how the Wii U would sell or when the NX would come. That said, if this comes out in 2016 for the series 30th anniversary, then I also imagine it would come out holiday 2016. So if the NX also comes out 2016, then it's possible for it to come out on both Wii U and NX. Even if it comes out early 2016, there could very well be a NX port when it launches. Point is, I don't think it'll be Wii U only, even if it is at launch.
Another thought is that Nintendo told SE about the NX during development, so development was then moved to NX knowing the Wii U's sales. This would mean a NX only title, and would likely launch at the NX launch in 2016 for the anniversary.
Then there's PlayStation. SE seems to really be pushing the PS4 with FFXV, KH3, Neir2, etc. If they had no problem releasing these on PS4 only (XBO is a non-factor in Japan), I don't see why they wouldn't the same with Dragon Quest. This rules out PS3/PS4 combo in my mind. I think SE realizes that the PS3 needs to die eventually.
Then there's Dragon Quest in general lately. It's been exclusive Nintendo after DQVIII was released. That said, recently Dragon quest Heroes was released on PlayStation platforms. Many thought this meant that Dragon Quest was going over to Playstation, But then DQVIII was announced for the 3DS. It's possible that DQ Heroes was on PS platforms because Koei/Omega Force wanted it there and that's the only reason it wasn't released on Nintendo stuff like all the other DQ games, we'll never know.
Another thing worth noting, if it isn't announced this year, it seems likely to me that it would be on NX since it isn't officially announced yet. It's possible that they announce Wii U this year and then later announce a NX port.
And then it's possible that it's on both console and handheld. So PS4/Vita, Wii U/NX/3DS, or NX/3DS. It's also possible the NX is a home console/handheld hybrid, so there's that. I doubt it personally, but it's a possibility nonetheless.
TL;DR: It'll probably be on either Wii U/NX combo, NX, or PS4 as far as consoles go. There may also be a handheld version along with it. None is more likely than the other as far as we can tell.
Also I have too much time on my hands.