The HD remake would have been released as a digital download, alongside Rare's Killer Instinct, according to former members of the development staff.
"We had an 'HD' downloadable version of TimeSplitters 2 in development at Free Radical in 2008," co-founder Steve Ellis told NES.
"I don't know what happened to that but yes, I'd love to see it released at some point. Maybe it could be the catalyst that is required in order to raise enough interest in TimeSplitters 4 that a publisher might want to fund it," he added.
During the same interview, former Rare artist Lee Musgrave revealed that Killer Instinct HD was also in the works, but faced licensing difficulties.
"Rare outsourced some of the conversion/development of Banjo Kazooie for Xbox Live Arcade, and it was kind of a test case for us to see what could be achieved in terms of developing with a partner, keeping our costs low and making some revenue," he explained.
"You can make your own conclusions as to how that turned out by the fact that we didn't move on to any of the other games you mention."
He added: "We came close to firing off a conversion of Killer Instinct a few times, but there were licensing obstacles to that, and it never really had enough perceived interest to push it forward."
The former Rare and Free Radical employees have since formed Crash Lab studio alongside Martin Wakeley, who previously worked for both companies.
Free Radical Design was purchased by Crytek in 2009. The company has firmly denied that a new TimeSplitters is in development.
Crytek has since hinted that TimeSplitters could return as a free-to-play game in the future.
Watch a video of TimeSplitters 2 below: