UPDATE: The name for this new title will be "Gyokugen Dasshutsu Adv: Zennin Shiboudes". "Gyokugen Dasshutsu" translates to "Extreme Escape". In Japan, 999 was named Gyokugen Dasshutsu: Ku Jikan, Ku Nin, Kyu no Tobira, which translates to "Extreme Escape: 9 Hours, 9 Persons, 9 Doors". Based on this title, the game could possibly take place in the 999 universe, but will not be a sequel to the original.
ChunSoft, the Japanese developer responsible for the well received and critically acclaimed adventure-puzzle-thriller known as "999" for the Nintendo DS, has announced that they will be making a successor to that title for the PSVita and the 3DS. This newly announced game will not be a sequel, but will be developed by the same staff. It will be fully voiced and will call upon some of Japan's best voice actors for the job. 999, which stands for 9 Hours 9 Persons 9 Doors, is considered one of the best, if not THE best title on the DS by owners of the system.
As of now, this is still a fresh announcement, so the details known are very vague. I will make sure to follow this title and post whenever new details are announced.