Cevat Yerli said that, although Crytek isn't currently working on the highly acclaimed shooter series, he personally wishes the company would, although a retail release is out of the question.
"Look, I wish we were working on it. I will say that," he told CVG in Los Angeles last week.
"I think hopes are high, but change has to happen in the platform space. I'm very excited potentially about the idea of a TimeSplitters for G-Face.
"The thing with TimeSplitters is, if we made a sequel to TimeSplitters, nobody would accept this apart from some fans, and we don't know how big the fan community is unfortunately.
"And we don't want to design this as a packaged goods game that launches on a console, and even if we wanted to I don't think publishers would like the idea. That is the truth, and that was the truth even before we bought Free Radical."
Crytek acquired Free Radical, the Nottingham based developer of TimeSplitters, in February 2009. Since then the company has faced persistent requests to return to the franchise.
Former Free Radical MD Steve Ellis previously said he shopped around the idea of TimeSplitters 4 to publishers and "nobody was interested" - a fact Yerli backed up.
"The concept behind TimeSplitters was pitched around before we took over and Free Radical had no luck. We think even on CryEngine and with Crytek behind it there would be fundamental issues with the concept," he said.
"However, TimeSplitters had one of the most fun multiplayer games ever, and G-Face is a social entertainment platform - it's about online gaming. I love the idea of a TimeSplitters for G-Face.
"I love the idea, and I wish we'll work on it, but currently we are not working on it."
One potential avenue for getting the game off the ground is the crowdfund platform Kickstarter, but Yerli expressed concerns over whether it would be appropriate for such a large company to call on fan funding.
"I've been asked this question internally and I said, 'how can we do a kickstarter? It wouldn't feel right.' I suppose if someone really, really wanted to...
"I guess the other issue is this; the reality also is we're quite a large company, but also we have capacity limits and we don't want to hire 15 people just to do this game. Kickstarter is a concept we thought about seriously... we'll see. Time will tell."
In my opinion, I hope this comes out. I would love to see the game which made my childhood of FPS come out but as a sequel. If this goes into kickstarter I'm sure to be donating loads. Though this is just my opinion of course.
