The BBC declined to comment, while Hungry Bear Media, who produces the show, has not responded.
Gray, a former English former rugby union and American football player, first appeared in the BBC reboot of the programme last year.
On Saturday, Gray told The Sun on Sunday: “There was an incident. That’s as much as I can say, until something comes of it and there’s action taken.
“Maybe there might not be. I’m still waiting to hear. The police are doing their thing.”
The newspaper reports that the BBC and Hungry Bear Media arranged for extra security around the Utilita Arena in Sheffield and outside the block of flats where he stays during filming.
The 6ft 5in (1.96m) star, from County Durham, recently revealed he often gets stopped by fans but finds the experience “really nice”.
“The show is universally loved by almost everybody,” he said.
First broadcast on ITV on 10 October 1992, Gladiators was like nothing seen before in the prime-time Saturday slot.
The Lycra-clad combatants, including Wolf, Warrior, Shadow and Cobra, became household names, while contenders took on an exhausting array of challenges.
The show ran on the network until 2000, before being resurrected by Sky between 2008 and 2009.
The BBC reboot in 2024 proved to be a ratings hit, with new Gladiators including Apollo, Sabre, Legend and Giant quickly becoming fan favourites.
Filming for the second series took place in Sheffield last August, and the show returned to BBC One and iPlayer this weekend.
