NEW YORK – There is something Donald Trump says he doesn’t know.

Trump has welcomed a reporter to his 26th-floor corner office in Trump Tower to talk about “All-Star Celebrity Apprentice.” And here in person, this one-of-a-kind TV star, billionaire businessman, ubiquitous brand mogul and media maestro strikes a softer pose than he has typically practiced in his decades on public display.

Relaxed behind a broad desk whose mirror sheen is mostly hidden by stacks of paper that suggest work is actually done there, Trump is pleasant, even chummy, with a my-time-is-your-time easiness greeting his guest.

He even contradicts his status as a legendary know-it-all with this surprising admission: There’s a corner of the universe he doesn’t understand.

The ratings woes of NBC, which airs his show, are on Trump’s mind at the moment, and as he hastens to voice confidence in the network’s powers-that-be (“They will absolutely get it right”), he marvels at the mysteries of the entertainment world.

“If I buy a great piece of real estate and do the right building, I’m really going to have a success,” he says. “It may be more successful or less successful, but you can sort of predict how it’s going to do. But show business is like trial and error! It’s amazing!”

He loves to recall the iffy prospects for “The Apprentice” when it debuted in January 2004. With show biz, he declares, “You never know what’s going to happen.”

Except, of course, when you do.

“I do have an instinct,” he confides. “Oftentimes, I’ll see shows go on and I’ll say, ‘That show will never make it,’ and I’m always right. And I understand talent. Does anybody ask me? No. But if they did, I would be doing them a big service. I know what people want.”

So maybe he does know it all. In any case, lots of people wanted “The Apprentice.” In its first season, it averaged nearly 21 million viewers each week.

And it gave Trump a signature TV platform that clinched his image as corporate royalty. He presided in a mood-lit stagecraft boardroom where celebrity subjects addressed him as “Mr. Trump” and shrank at that dismissive flick of his wrist and dreaded catchphrase, “You’re fired.”

The two-hour premiere of “All-Star Celebrity Apprentice” (Sunday at 9 p.m.) starts by rallying its 14 veteran contenders in the even more evocative setting of the 2,000-year-old Egyptian Temple of Dendur at the Metropolitan Museum of Art.

There, grandly, Trump receives such returning players as Gary Busey, Stephen Baldwin, LaToya Jackson and reality mean queen Omarosa.

Soon, teammates are chosen by team leaders Bret Michaels and Trace Adkins. Their first assignment: concoct a winning recipe for meatballs, then sell more of them than the rival team.

This is the 13th edition of the “Apprentice” franchise, which has now slipped to less than one-third its original viewership, according to Nielsen Co. figures. But even an audience matching last season’s 6.26 million viewers would be pleasant news for NBC, which has recently fallen to fifth place in prime time, behind even Spanish-language Univision.

“I could probably do another show when I don’t enjoy ‘The Apprentice’ anymore,” says the 66-year-old Trump, mulling his TV future. “I have been asked by virtually every network on television to do a show for them. But there’s something to sticking with what you have: This is a good formula. It works.”

Years before “The Apprentice,” Trump had hit on a winning formula for himself: Supercharge his business success with relentless self-promotion, putting a human face – his! – on the capitalist system, and embedding his persona in a feedback loop of performance and fame.

Since then, he has ruled as America’s larger-than-life tycoon and its patron saint of material success. Which raises the question: Does he play a souped-up version of himself for his audience as Donald Trump, a character bigger and broader than its real-life inspiration?

He laughs, flashing something like a you-got-me smile.

“Perhaps,” he replies. “Not consciously. But perhaps I do. Perhaps I do.”

It began as early as 1987, when his first book, “Trump: The Art of the Deal,” became a huge best-seller.

And even without a regular showcase, he was no stranger to TV. For instance, in the span of just 10 days in May 1997, Trump not only was seen on his “Miss Universe Pageant” telecast on CBS, but also made sitcom cameo appearances as himself on NBC’s “Suddenly Susan” and ABC’s “Drew Carey Show.”

Meanwhile, as a frequent talk-show guest then (as now), he publicized his projects and pushed his brand.

“I’ll be on that show for 20 or 30 or 60 minutes, and it costs me nothing,” he notes. “When you have an opportunity for promotion, take it! It’s free.”

Trump even seems to profit from the harsh attention focused on his hair.

“I get killed on my hair!” he says, with no trace of remorse. But he wants everyone to know, “It’s not a wig!” Nor is it an elaborately engineered coif to hide a hairline in retreat, as many Trump-watchers imagine.

To prove it, Trump does a remarkable thing: He lifts the flaxen locks that flop above his forehead to reveal, plain as day, a normal hairline.

“I wash my hair, I comb it, I set it and I spray it,” he says. “That’s it. I could comb it back and I’d look OK. But I’ve combed it this way for my whole life. It’s become almost a trademark. And I think NBC would be very unhappy if I combed it back, ’cause – you know what? – maybe I wouldn’t get as high a rating.”