A source told The New York Times that a White House aide asked South Dakota Gov. Kristi Noem (R) last year how an interested party might go about adding another giant presidential face to the national monument that bears the likeness of four of the country’s most famous leaders.

Mr Trump on Monday dismissed the report as “fake news” in a tweet, but went on to hail the achievements of his presidency.

He tweeted: “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!”

Mr Trump has reportedly speculated before about having his face on Mount Rushmore alongside George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln.