Crytek founder and CEO Cevat Yerli said he loves "everything" about the franchise, but publishers don't feel the same way.
"I wish we would develop it. We can't develop it the way Free Radical had started it before we acquired them," he told Videogamer.
"When we looked at it - and again, I love TimeSplitters, I'm a huge TimeSplitters fan particularly of the multiplayer part.
"I love the idea, I love the brand, I love everything – but the publishers don't. That's reality. And I don't want to spend our own money on the project in a retail business."
Yerli continued that he would "love the picture" of the franchise running on Crytek's free-to-play service GFACE, adding: "So if we get enough fans being loud enough..."
Last month, Crytek firmly denied that TimeSplitters 4 was in development.
It followed a report that a magazine has seen TimeSplitters 4 in action.
Last year, both the game and a new Xbox were rumoured for a 2012 reveal, which was promptly denied by Crytek.
Watch a video of TimeSplitters: Future Perfect below: