Update: some footage

https://www.youtube.com/watch?v=2cVViGz9ato

Update showing the Compound map. Nothing special, but includes an awesome remix of Neotokyo for the music :P

He also talks a bit more about PS4 version in the comments. Still not confirmed sadly:

"PS4 is the console we want, if we can get it."

Original story

TimeSplitters Rewind, a collection of maps, weapons and characters from the three previous TimeSplitters titles in the series, is in development for PlayStation 4 systems by a team of around 35 part-time developers, project lead Michael Hubricka told CinemaBlend.

However, this doesn't mean the multiplayer title, which is powered by CryEngine 3, will necessary make it to retail. According to Hubricka, the development team is working to obtain approval from Crytek's legal department in order to release the game on Sony's console.

"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. 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 [then] start something for the PlayStation 4," he said.

"So we decided that since they released the SDK to allow us to do this, we're going to go ahead and do it ourselves, and when they say 'yes' or 'no' we can decide what to do with that. For now we're just going to go ahead and do it. So at least we're prepared".

A playable alpha is slated for release later in the year. According to Hubicka, they team is roughly 20 percent done with the game, but plans on releasing playable parts as they become available, with characters, maps and weapons scheduled to arrive later on.

http://www.polygon.com/2013/9/3/4689062/timesplitters-rewind-is-in-development-for-ps4

UPDATE

AMA with the project manager of the game:

http://www.reddit.com/r/Games/comments/1lo5mp/i_am_michael_hubicka_project_manager_of/

I really, really hope Crytek allow this.

Just the thought of playing Virus again gets me pretty excited!

Can't have too high of hopes for this if they only have part-time workers on the project.

Fingers crossed.

Hmm never played Timesplitters game myself, but they are critically acclaimed so maybe I would give them a chance on the PS4. Still, Crytek is not all over PS platforms lately so if they didn't get aproval yet, then there might be a reason for it.

I remember it playing split-screen with four players on PS2 with a Multi-tap on a small CRT screen and still having some fun :p

Now this sounds interesting. Loved Timesplitters 2, didn't get to play it much multiplayer though.

Pls make it

YES YES YES YES!

Don't have much faith in Crytek sadly.