Absolutely a 25th Century show, mostly because it allows the writers to re-establish the area. Not get tied down by the continuity and politics of the old shows. That's the real reason TNG jumped 80 years, to remove the shackles of what TOS and the films had put them in.
For it to be Star Trek and stand on it's own, just like TNG did, it would have to be a new frontier. A ship out there Boldy Going Where No One Has Gone Before, which is absolutely what a new show must be about. Feasibly it could be the same galaxy, with the Gamma Quadrant pretty unmapped, but it gets a little murky. I think the best chance for that is either the Federation can now travel to a new Galaxy, or you go with something along the lines of the premise of the aborted pitches of Bryan Singer's Federation or animated series Final Frontier.