While it doesn't look like we're likely to see a new TimeSplitters game anytime soon, Homefront: The Revolution will offer a rather significant Easter egg when it launches this May. You'll be able to play the first two levels from TimeSplitters 2, via an arcade cabinet you can find in the game.
Apparently, the arcade cabinet with the playable Siberia and Chicago levels from Free Radical's manic FPS classic can be found in a prison area located in Homefront: The Revolution's expansive open world. TimeSplitters 2 launched for PS2, Xbox and GameCube back in 2002.
The last TimeSplitters game to see the light of day was TS2 follow-up, Future Perfect in 2005. Since then, rumours and speculation have been rife regarding a TimeSplitters 4, which has failed to materialise. Homefront: The Revolution developer Dambuster Studios was formerly Crytek UK, and Free Radical before that.
Crytek bought the studio before Deep Silver acquired it and renamed it, meaning that
Crytek still owns the rights to the TimeSplitters series. So, while this Easter egg means we get to revisit TimeSplitters, it doesn't necessarily signal that a new game is in the offing *cry*.