In an interview with Famitsu, Square Enix revealed that it has no plans for a Chrono Cross sequel or a new title within the franchise. However, alongside this, Square Enix also stated that “no one knows what the future holds” regarding potential future works. This information comes from an interview with Masato Kato, Yasunori Mitsuda, and Nobuteru Yuki. Square Enix provided a direct response to the inquiry about potential sequels or new installments after the release of Chrono Cross: The Radical Dreamers Edition. [Thanks, ryokutya 2089!]
This is what Square Enix had to say specifically:
There are no plans for (a sequel or new title) now, but no one knows what the future holds.
This information comes just ahead of the release of Chrono Cross: The Radical Dreamers Edition. This is a remaster of the title which features improved graphics and includes additional arranged tracks. The remaster also features an entirely new song that was not in the original release of the game. Square Enix has also shared several visuals that highlight improved graphics and new fonts that will be available with the remaster.