Crytek owns the TimeSplitters IP, but it doesn't appear Crytek is interested in making a new game in the series--lest it be free-to-play. The fan-made (and Crytek-approved) TimeSplitters Rewind project restores multiplayer maps based on the previous three games in the series in the CryEngine. While it's destined for PC release, the development team is already starting work on a PS4 version.
"We're actually going to go ahead and start development [of Timesplitters Rewind] on PlayStation 4, just because we're pretty confident Crytek's going to say go ahead and do it," project lead Michael Hubicka told Cinema Blend (via CVG). "But we don't want them saying go ahead and do it when we're caught with our pants down and we're like halfway through development and start something for the PlayStation 4."
TimeSplitters Rewind is currently in pre-alpha and footage can be seen in the video below. Hubicka is not committing to a release window, but hopes to reach alpha before the end of 2014.