Donald Trump called the New York Times report "fake news" but said the suggestion "sounds like a good idea".
US President Donald Trump has denied reports his administration reached out to the governor of South Dakota about adding him to Mount Rushmore.
Last year, a White House aide contacted Kristi Noem’s office asking about the process of carving additional presidents onto the monument, the New York Times reported, citing a Republican official familiar with the conversation.
Mr Trump has since responded to the report, calling it “fake news” but adding the suggestion “sounds like a good idea”.
“Never suggested it although, based on all of the many things accomplished during the first 3 and a half years, perhaps more than any other Presidency, sounds like a good idea to me!” he wrote on Twitter.
A White House official had previously told The Times Mount Rushmore is a federal, not state, monument.
Mount Rushmore National memorial is a huge sculpture carved into the granite face of Mount Rushmore in the Black Hills region of South Dakota.
Its granite faces depict US presidents George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln, and is said to tell the story of “birth, growing, development and preservation" of the country. But some native leaders have long criticised its history and called for the removal of a site that is carved into sacred land.
Ms Noem has previously said it was Mr Trump’s "dream" to have his face etched on Mount Rushmore.
The Times report suggests Ms Noem worked to ensure the president would make a visit to the monument ever since she was elected governor of South Dakota in 2018.
According to a 2018 interview, Ms Noem said the pair had a conversation during their first meeting at the Oval Office.
“He said, ‘Kristi, come on over here. Shake my hand,” Ms Noem said.
“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?’”
Ms Noem said she started laughing.
“He wasn’t laughing, so he was totally serious,” she said.
Last month, Mr Trump visited Mount Rushmore to deliver his 4 July speech during which he defended the monument as “an eternal tribute to our forefathers and to our freedom”.
“This monument will never be desecrated, these heroes will never be defaced, their legacy will never, ever be destroyed, their achievements will never be forgotten, and Mount Rushmore will stand forever as an eternal tribute to our forefathers and to our freedom,” he told the crowd of supporters.
Introducing the president that night, Ms Noem likened him to Theodore Roosevelt and also went on to hit out at protestors.
According to The Times, which cited a person familiar with the episode, she also gifted him a four-foot replica of Mount Rushmore that included his face.