"Everybody who gives even a hint of being a 'birther' ... even a little bit of a hint ... they label them as an idiot," Trump told ABC's "Good Morning America" in an interview aired Thursday.
A "birther" is someone who argues Obama is not a natural-born U.S. citizen and is therefore not eligible to be president.
"Let me tell you, I'm a really smart guy. I was a really good student at the best school in the country," said Trump, who attended the University of Pennsylvania's Wharton School. "The reason I have a little doubt -- just a little -- is because he grew up and nobody knew him.
"If I got the nomination, if I ever decide to run, you may go back and interview people from my kindergarten. They'll remember me," Trump said aboard his private Boeing 727.
By contrast, "Nobody comes forward" to say they knew Obama as a little boy, Trump said. "Nobody knows who he is until later in his life. It's very strange."
Hawaii Gov. Neil Abercrombie has said he knew Obama's parents in Hawaii and remembers when the future president was born. Abercrombie, a Democrat, initially said he would produce an original copy of Obama's birth certificate but didn't because it's against state law to release private documents, ABC News quoted his spokeswoman as saying.
The Obama campaign produced a certification of live birth in 2008 that reported his birthplace as Honolulu.
Obama attended kindergarten there before moving to Jakarta with his stepfather at age 6.
Katherine Nakamoto, Obama's kindergarten teacher, described "Barry" Obama, at age 5, as "a cute, likable, heavy-build child."
"I could visualize Barry smiling, dressed in his long-sleeved, white shirt tucked into his brown Bermuda shorts, and wearing laced shoes," she told The Maui (Hawaii) News in a story published Jan. 21, 2009. She also provided a photo she said was taken in 1967 of Obama's kindergarten class.
Some "birthers" allege Obama was born in Kenya, not Hawaii, or that his birth certificate is a forgery. Others allege he's a citizen of Indonesia or that because he had dual British and U.S. citizenship at birth, he was not a natural-born citizen.
Chester Arthur, a Republican U.S. president from 1881 to 1885, was also a British subject as well as a U.S. citizen at birth.