A White House official has made discreet inquiries into the possibility of Donald Trump’s image being carved into Mount Rushmore.

According to The New York Times, the official, who was not named, approached the office of Kristi Noem, the South Dakota governor, last year to ask how an additional President could be added to the monument.

Details of the approach emerged over the weekend. Likenesses of four Presidents — George Washington, Thomas Jefferson, Abraham Lincoln and Theodore Roosevelt — were immortalised in the massive 1941 sculpture which took 14 years to create.

The attraction in the Black Hills has more than 2 million visitors a year.

Trump first raised the possibility of being added to the pantheon of US presidents when he met Noem at the Oval Office as far back as 2017.

The South Dakota governor assumed the President was joking, she recalled a year later.

“He said, ‘Kristi, come on over here. Shake my hand’. 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. He wasn’t laughing, so he was totally serious.”

The South Dakota governor did present Trump with four-foot replica of Mount Rushmore — with his face added — when Trump visited the state early last month.

The chances of Trump’s dream becoming a reality are considered slim, given the lack of usable rock on either side of the existing likenesses.

The kerfuffle over Trump’s desire to carve his way into history was the culmination of a difficult weekend for the President.

On Saturday he abruptly ended a news conference after being challenged over claiming credit for passing the Veterans Choice Programme, which made it easier for former servicemen and women to get medical care.

The legislation was passed in 2014 and signed by Barack Obama.