Trump said he and fellow executive producer Mark Burnett are weighing a stage musical based on the NBC reality series about competition among corporate jobseekers.
"We are really looking at it and we've had a lot of interest from Broadway," Trump said Tuesday.
The real estate mogul, known for excess rather than understatement, predicted a musical adaptation "would be a smash." The proposal is being shaped, he said, promising more details later.
In an NBC telephone news conference, he also predicted more success for the hit TV show that gave birth to his trademark phrase, "You're fired!"
The latest version, which begins with a 90-minute episode 8:30 p.m. EST Thursday, pits nine college graduates against an equal number of entrepreneurs with high school diplomas in what NBC is billing as "book smarts against street smarts."
Trump, who attended the University of Pennsylvania's Wharton School of business and calls himself a believer in the value of education, said he was impressed by the skills of the non-college contestants.
They are "maybe more driven because they have a little chip on their shoulder," he said.
The series' prize is a job with a Trump enterprise.
Asked if he felt pressure to hire a woman after the first two seasons ended with male winners, Trump — who's getting married for the third time on Saturday — said no.
"The women have done very well on the show ... in many cases better than the men," he said, adding: "I can't think like that, because then it just becomes statistically who's going to get in."
Trump is signed through this season and said NBC "wants to renew my contract very badly." He probably will remain with the show through the fifth season, he said, with the deciding factor being its continued success.
The series finished last season as one of the top programs among advertiser-favored young adult viewers, Trump boasted.
But it did show signs of slipping, as the audience for the second-season finale dropped 39 percent compared to the first year.
Trump questioned how "The Apprentice" would fare without him holding court in the boardroom.
"It's not going to be so easy to replace me. I wouldn't want to replace me," he said.
Besides, Trump, who's heard "You're fired!" yelled at him regularly from taxis and even in a Trump resort locker room, conceded: "There's something very seductive about being a television star."