Square Enix has renewed the trademark for Parasite Eve recently in Europe. This could hint at the resurrection at the series.
Parasite Eve has received two mainline games on the PS1 and it was followed by a lackluster third entry that took a dramatic approach to gameplay. It was bashed by almost every critic and basically killed the series for good.
The new trademark renewal (via) seems to be mainly in Europe and it could be just your standard procedure. It can also point towards Square Enix having plans for the franchise in the near future so they keep renewing it once they have something in the works. As for what it could be, we can only hope that it ends up being more of the classic games instead of the third entry.
Parasite Eve has enjoyed a cult classic status because of its unique blend of survival horror with JRPG aesthetics. It also featured full motion videos which looked great for their times and followed the Final Fantasy approach of mixing gameplay with these FMV videos.
Parasite Eve 1 and 2 are available for the PS1 while Parasite Eve 3 was more of a spin-off titled as The Third Birthday. It was released exclusively for the PSP.