"There is never going to be a tape that shows up," Trump told "Fox & Friends" co-host Ainsley Earhardt. "There is never going to be anything that shows up. I would be very embarrassed if a tape showed up. I would be doubly embarrassed. There is no tape."
The dossier, written by a former spy from Britain’s intelligence agency, was commissioned by Republican and Democratic operatives during the presidential campaign.
It was first given to the FBI in August by Democratic political operatives who shared it with news organizations, including ABC News. Among the unsubstantiated claims are allegations that Trump was personally compromised by the Russians during a 2013 trip to Moscow.
In the same interview, Trump said he isn't a fan of tweeting, explaining that he uses Twitter to defend himself against the "dishonest media."
"Look, I don't like tweeting," Trump said. "I have other things I could be doing. But I get very dishonest media, very dishonest press. It's my only way that I can counteract."
He continued: "When people misrepresent me because the press is very dishonest, unbelievably dishonest, when people misrepresent me, I have at least a way of saying it's a false statement. If the press were honest, which is not, I would absolutely not use Twitter. I wouldn't have to."
Trump also addressed criticism about the lack of A-list celebrities participating in his inauguration events.
"Many of the celebrities that are saying they're not going, they were never invited," he said. "I don't want the celebrities, I want the people, and we have the biggest celebrities in the world there."
Turning to Obamacare, the president-elect promised that his team will come up with an affordable alternative.
"We're going to have a plan that's going to be great for people," he said. "And it's going to be much less expensive. And you will be able to actually have something to say about who your doctor is and your plan."
Trump added: "Nobody is going to be dying on the streets with a President Trump. We want to take care of everybody."
ABC News' Alex Mallin contributed to this report.