"He said it. 'Grab ’em by the pussy,'" Bush wrote in an editorial published in the New York Times on Sunday.
The New York Times reported last month that Trump has been privately telling aides and allies, including at least one U.S. senator, that the voice on the recording was not his.
That would be a reversal from his immediate acknowledgement of responsibility after the tape surfaced weeks ahead of the 2016 presidential election. Trump said: "I said it, I was wrong, and I apologize."
Reuters has not been able to verify the Times report that he has been privately telling allies a different story.
The White House did not immediately respond to a request for comment on Bush's remarks. But White House spokeswoman Sarah Sanders played down the Times report at a White House briefing on Nov. 27.
"The President hasn't changed his position. I think if anything that the president questions, it's the media's reporting on that accuracy," Sanders said.
Bush laughed on the video as Trump spoke and he lost his job as a host of NBC's flagship morning "Today" show after the tape was leaked to the media in October, upending Trump's campaign to become president.
Thumbnail Credits : REUTERS/Steve Marcus