David Sneddon disappeared in 2004 while traveling in China's Yunnan province, Voice of America reported.
His father, Roy Sneddon, of Providence, Utah, says the family is "quite confident that David is alive, quite confident that whatever the mechanism that got him there he is in North Korea."
North Korea in the past has abducted many people outside the country, including dozens of Japanese people, VOA said. Those detained have been used to teach language and culture to spies.
David Sneddon's mother, Kathleen Sneddon, shares her husband's belief that her son could be alive in North Korea.
"His abduction fits a pattern of the way North Korea does it. He came to that restaurant -- a Korean restaurant -- and said goodbye to them and then disappeared in a few hours," she explained. "He's a perfect candidate to be taken because he speaks Korean fluently and was studying Mandarin Chinese at the time, and of course [he speaks] English. If they're looking for an English teacher, which is one of the theories, then he was a great candidate for it."
The U.S. State Department said no evidence points to David Sneddon having been abducted by North Korea.
The State Department said the U.S. Embassy in Beijing and its consulate in Chengdu have been in "regular, ongoing contact with local authorities" about David Sneddon's disappearance in August 2004, and "will follow up on any new evidence in coordination with local authorities."