"Everybody's speculating on my retirement and I don't know why," Trebek told the Los Angeles Times.
"It's silly," said Trebek, who is 72 and will be 76 when his contract is up in 2016.
"Somebody asked me if I've given any thoughts to retiring," he told the Times. "Well, yes, I've given thoughts to retiring, for crying out loud. I've been doing the show for 29 years. Why wouldn't I think about retiring?
"Everybody assumes from my having said that, that he's retiring," Trebek said. "Well, no. I've been thinking about it. So allow me to think about it."
The New York Post reported last month "Jeopardy!" production company Sony Pictures Television was considering NBC "Today" show host Matt Lauer to replace Trebek starting in the 2016-2017 season.
Additional names mentioned by online magazine Deadline.com are NBC News anchor Brian Williams, CNN anchor-reporter Anderson Cooper and NBC sportscaster Dan Patrick.
Trebek, who has won five Outstanding Game Show Host Emmy Awards and a star on the Hollywood Walk of Fame for his "Jeopardy!" work, said he still likes hosting the show, in which contestants are presented with clues to a wide variety of topics in answer form, and they must phrase their responses in question form.
But he said when he does want to leave, people should not expect to receive much notice.
"It'll probably happen very quickly," he told the newspaper. "There won't be any fanfare. It'll be like the time I shaved my mustache on a whim. I'll just ask the director to leave me 20 or 30 seconds at the end of the program to say a few words and I'll say a few words and thank people and be on my way."