However, Trump did say that adding his face to Mount Rushmore "sounds like a good idea."

Donald Trump has denied that White House aides reached out to South Dakota Gov. Kristi Noem last year about the process of adding additional presidents to Mount Rushmore.

On Sunday night, Trump took to Twitter to address a recent report done by the New York Times, which said that a Trump administration official had asked about adding presidents to the national monument last year.

"This is Fake News by the failing@nytimes& bad ratings @CNN," he wrote. "Never suggested it although, based on all of the many things accomplished during the first 3 1/2 years, perhaps more than any other Presidency, sounds like a good idea to me!"

Prior to that tweet, Trump had shared a picture of him in front of Mount Rushmore, which was taken from his Fourth of July celebration there this year.

Trump had previously voiced his want to have his likeness a part of the national monument to Gov. Noem during the two's first meeting in the oval office.

"He said, 'Kristi, come on over here. Shake my hand,'" Noem recounted to South Dakota's Argus Leader. "I shook his hand, and I said, 'Mr. President, you should come to South Dakota sometime. We have Mount Rushmore.' And he goes, 'Do you know it's my dream to have my face on Mount Rushmore?' "I started laughing," she said. "He wasn't laughing, so he was totally serious."

As the Times noted in its recent report, Noem greeted Trump with a four-foot model of Mount Rushmore with his face carved into it when he visited the monument in early July.