Squidix has fallen on somewhat rough financial times. Nothing like Square right after "Final Fantasy The Spirits Within" and right before the merger with Enix, but they're not doing great either. FF13 had decent sales leavened with a moderate amount of criticism, FF14 completely tanked under a mountain of criticism and Squidix is desperately trying to dig their way out. (And if you haven't been following the situation, that last bit is not in any way an exaggeration. There's pretty much universal acceptance that the FF14 launch was an epic failure, the only question is if they can manage to fix things enough to keep even a modest player base.) In the wake of all that Squidix announced that they're expecting something like a $150 million loss for the fiscal year.
That's factored into the speculation about FF7 remakes a lot. "This is the kind of financial crisis they've been holding the FF7 remake back for! Now they can just cash in on it!"
Now on the other hand, Nintendo is coming out with a new console. They've got wheelbarrows full of money to spend marketing it. How much money would Nintendo have to offer Squidix for them to actually remake FF7, and make it a timed exclusive on the Nintendo Cafe?
A lot of older "hardcore" gamers consider the original Final Fantasy 7 to be the prime event signaling the decline of Nintendo as a "hardcore" gaming company and the rise of Sony. Actually it was a rather singular event in a lot of ways. Final Fantasy was always big in japan of course, but in America it had a much smaller audience. Nintendo losing the franchise to Sony was a big shock to that group of fans, but then Sony really pushed it as the kind of flagship RPG for the PSX, and it really took off. There's a definite discontinuity in the FF fandom between those who were in before FF7 and those who got started with it. (I'm not going to argue there's some kind of merit to one side or another, just that the fandom is aware of the grouping.) So in some ways Nintendo losing Final Fantasy made both the Final Fantasy series and the Playstation big in America. And a lot of "hardcore" gamers feel that Nintendo has been gradually disappointing them more and more ever since. Each console since then has had less "hardcore" games, and less "big" third party games in general. This has reached its current peak with the Wii. Not only has the dearth of third party games continued, but Nintendo's emphasis on trying to capture the "casual" market has left a lot of "hardcore" gamers feeling alienated and making disparaging comments about "waggle" mechanics.
So if Nintendo wanted to recapture the enthusiasm of the "hardcore" market (and marketing research on attach rates seems to indicate that it's a good thing to have a core of "serious" gamers supporting you system even if you've also got a wide pool of "casual" gamers) getting a FF7 exclusive would certainly be a way to do it, especially if they could in some way take credit for convincing Squidix to do it.
Is it going to happen? I seriously doubt it. It would be a brilliant marketing move for Nintendo and would make a lot of money for Squidix (though i'm doubtful about whether they could actually create a good FF7 remake at this point) but i expect both companies are far too proud and stubborn for it to happen. Squidix has been resisting for so long that i doubt they'd capitulate just for the sake of wheelbarrows of money when they're not in truly dire need, and it's entirely possible that Nintendo is still feeling bitter about the original "betrayal" all those years ago. (I know harsh words were exchanged about it for quite awhile afterwards, though i don't know how much Nintendo's internal corporate culture has evolved since then.)
Failing that, i'm not sure if there's any other companies that Nintendo could cut a similar deal with. A company that's popular amongst the "hardcore" and is a major player on other consoles, but isn't big enough in America to write it's own ticket. Perhaps making a big deal with NIS, Atlus, or possibly Level 5? The problem is that the market has gotten so big since the days of the SNES/PSX transition, gamers are a lot more informed than they used to be, and the "hardcore" is no longer as unified as it once was. There are "hardcore" RPGers, "hardcore" FPS gamers, "hardcore" third person action-adventure gamers, "hardcore" strategy gamers, "hardcore" sports gamers, etc. A lot of people belong in more than one category, but there's no category that will cover all or even most gamers. (FPS probably comes closest, as much as it pains me to say so, but that's also the category with the most competition from well established companies and franchises.)
It would certainly fit thematically if Nintendo suddenly announced that Disgaea 5 was going to be a Nintendo Cafe exclusive and made a big advertising push and all of the sudden millions of American games said "OMG! I'd never encountered this strategy RPG thing before, but now i'm totally hooked!" and NIS suddenly became a big name in America, but somehow i don't see that happening :)