Square Enix has registered a trademark in Europe for Parasite Eve, and while there is no other information beyond that itself, it seems likely the Japanese compay might be thinking about launching a brand new entry in the acclaimed series, or at the very least a full-blown remaster of the Parasite Eve trilogy. We expect there will be more details on this soon, after the project is announced in the future.
Considering that Final Fantasy IX and XIV, and even Kingdom Hearts HD 1.5 + 2.5 have been ported and are available on the current-gen consoles now, we may get a Parasite Eve remaster for Xbox One and PS4 at some point. Let's not forget that Square is also actively developing the remake of Final Fantasy VII that was officially announced at E3 2015, but this one might launch for the next-gen systems.
The Parasite Eve trilogy contains three games - Parasite Eve, Parasite Eve II and The 3rd Birthday. The first games were released in 1998 and 1999 respectively, giving the player a chance to control police officer Aya Brea, who tries to understand the origin of the titular Eve, an ancient evil that threatens all life on Earth. The series’ spin-off 3rd Birthday was a PlayStation Portable exclusive that his stores in 2010, continuing the story of Aya and her dangerous quest to regain her lost identity and memories.