Donald Trump says it would be a ‘good idea’ to add him to Mount Rushmore following claims that his office contacted the governor of South Dakota Kristi Noem to discuss the idea.

The President has denied that an approach was made to add him to the famous monument following claims made by the New York Times.

Trump branded the report ‘fake news’ and said he ‘never suggested it,’ but added that because of his ‘many accomplishments’ during his first term as president that it ‘sounds like a good idea’.

He said on Twitter: “This is Fake News by the failing @nytimes & bad ratings @CNN. 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!”

Noem had previously claimed that in 2017 Trump told her it was his ‘dream’ to have his face on Mount Rushmore during their first meeting in the Oval Office after he was made President.

The world-famous 60-foot-tall sculpture took 14 years to create and opened in 1941. It features the faces of four US presidents -  George Washington, Thomas Jefferson, Abraham Lincoln and Theodore Roosevelt.

It is in the Black Hills which attracts more than two million tourists a year and there have been suggestions to add the likes of  Franklin Roosevelt, John F. Kennedy, Ronald Reagan and Barack Obama.

But Maureen McGee-Ballinger, public information officer at the site, said ‘there is no more carvable space up on the sculpture’.