It’s hard to imagine a celebrity who’s eager to perform anonymously. But that’s exactly what’s happening when Fox unveils its new show, “The Masked Singer,” on Jan. 2.

Garbed in outlandish costumes that obscure their identity, famous stars compete on the stage with others equally anonymous, while a panel and the audience tries to blow their cover.

The show, which is a big hit in Asia, pits 12 “singers” against each other — two performing opposite each other in segments. One singer will be eliminated each week and will, at last, reveal their identity. The contenders aren’t all singers, either. According to Nick Cannon, who hosts the show, rivals represent 65 Grammy nominations, 16 Emmy Award nominations, 16 multi-Platinum Awards, four Super Bowl titles and four stars on the Hollywood Walk of Fame.

The studio panelists include Jenny McCarthy, Robin Thicke, Ken Jeong and Nicole Scherzinger, who oversee the performances and try to guess who the secret singer is. McCarthy says the talent behind the elaborate costumes could be executing a routine they’ve never done before. “They could be an actress that we never knew had a singing voice,” she says.

“So that’s what was so fun in trying to figure out who they were, because a lot of them looked like they’d been doing this for their whole lives, and we found out this was the first time they’ve done it on stage.”

Jeong, who starred in his own sitcom, “Dr. Ken” on ABC, says he wanted to participate because the Asian version is his mother’s go-to show. “I’m Korean, and this is my mother’s favorite show in Korea. No joke,” he says. “So when Fox invited me to be a part of this show, it was as simple as that. My mom was like, ‘You HAVE to do this show.’ And she showed me all these YouTube clips. It’s like billions of views on these YouTube clips. And I was like, ‘I’m in.’ ”

The entire production is shrouded in super secrecy. Even the families of the participants don’t know they’re one of the masked singers. “No one knows who any of these people are,” says Cannon. “So even when they drive onto the lot, it’s, like, secret service is taking them into this cave.”

Cannon, who’s hosted shows like “America’s Got Talent,” insists, “I don’t host anything unless I’m thoroughly enjoying it. So when I saw the tapes, I said, ‘That looks like a good time. It looks so much fun.’ I get to wear my crazy shoes and outfits and don’t seem out of place,” he says.

“It’s not just a singing competition. It is a mystery show. It has a game element. It’s extremely hilarious. It’s the true essence of what variety is. And anything you have ever seen me do in my career, I like to be able to implement everything I do as a multifaceted entertainer.”

The costumes are so intricately designed that there’s no chance of identifying the person behind the mask until the unveiling. And each entertainer gets to pick their costume, says Izzie Pick Ibarra, the show’s executive producer and one of the creators of “Dancing with the Stars.”

While they are amazingly deceiving, the costumes are also difficult to manage, says Ibarra.

“Some of them had very limited vision with the mask on. And your peripheral vision basically disappears. So trying to then perform on stage with lights shining, wearing a mask and an incredibly kind of heavy costume, it took some skill to do that.”

Elaborate measures have been taken to protect the identity of the entrants. No one knew, says Ibarra, not even the crew.

McCarthy agrees. “I went around pressing cameramen and everyone, being so nosy, going, ‘Do you know?’ ‘Do you know?’ And no one knew. I mean, the secrecy made it that much more fun, even for us, to try to figure out.”