I think it will, and should, though not in the near future.
Cost and time are irrelevant, the game would be changed so much (to be at 13/15's standards) that it will be equivalent and treated as a "new" game, this isn't a problem, it's just a way to skirt around the issue of reputation/morale. On changing things, I'm currently replaying 7 for the millionth time alongside 8/9/13-2/LR and X/X-2 HD (I know...) and some of the more comedic scenes would be hard to reproduce, so hard that they would be almost totally different, due to original models having basically no real facial or body animations outside of the few limited ones, things like Don Corneo bouncing ontop of the bed and bouncing around to be reproduced in 3D and at a different perspective would have to be totally retooled and changes to the script for voice over, and quality purposes.
Now for me personally, I think they should remake 8 and 9 first, for a few reasons, putting opinions aside, neither are bad games, 9 especially, 9 would make a fantastic remake because it's so damn creative and beautiful, Hironobu Sakaguchi himself has said that it is his favourite Final Fantasy, the one that represents the closest vision to the "true" Final Fantasy, alongside being the one that would deserve a squeal more. So by remaking 9, or 8, first, they can test the waters, the reaction of such a massive change in graphics and perspective, the retooling of scenes and script editing (Story shouldn't be touched, but several scenes in all 3 games would need rewrites to come across properly in a remake with highly detailed scenes and characters), they can see the fan reaction, see the media reaction, the reviews, and sales, without the risk of tarnishing the "holy grail" of FF7. < Fun fact, iirc, they considered remaking 9 on PS2 a year after it was released, and it got cut.
I think G-Bike, and possible other games based on the Golden Saucer could indeed be leading upto a remake, the original fans of FF7 are getting old, a lot don't have time to put 100 hours into a game anymore, so building up a fanbase in the massive mobile market, with new customers, making them interested in the world of FF7 is a great step towards the "final goal". So whilst they are building up a new fanbase in the future with FF7 spin-offs, in what is frankly, a much larger market, will it be enough to replace old FF7 fans who, if given enough time, simple won't care about the remake they have craved so long?
Regardless, a remaster should be handled by SE themselves, whilst the FFX remaster was great (imo), a lot of LR was handled by an outsourced company, and the flat background textures and buildings look absolutely awful in comparison to Lightning and monsters.
Edit: Funny, watching the new Dragon Quest Heroes trailer for PS4, is pretty similar to how I'd imagine an FF9 remake.