The participation of Tiegs, a former supermodel and True Beauty judge, was reported by Entertainment Weekly, which also reported that Andretti, a racecar driver, will be part of the cast.
The castings of Aiken, who finished second on American Idol's second season in 2003, and Gibson, an 1980's teen singer turned actress, were reported by People, while Gotti's inclusion in the cast was reported the New York Daily News.
Gotti is the daughter of the late Gambino crime family John Gotti. She previously starred on Growing Up Gotti, a reality series which aired two seasons on A&E in 2004 and 2005.
The Celebrity Apprentice's fifth season is scheduled to begin filming in New York City this month and premiere on NBC early next year.
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