From The New York Times:
After all, the president had told her in the Oval Office that he aspired to have his image etched on the monument. And last year, a White House aide reached out to the governor’s office with a question, according to a Republican official familiar with the conversation: What’s the process to add additional presidents to Mount Rushmore?
In private, the efforts to charm Mr. Trump were more pointed, according to a person familiar with the episode: Ms. Noem greeted him with a four-foot replica of Mount Rushmore that included a fifth presidential likeness: his.
The current presidents on the monument, from the National Park Service:
George Washington, First President of the United States
“The preservation of the sacred fire of Liberty, and the destiny of the Republican model of Government, are justly considered as deeply, perhaps as finally staked, on the experiment entrusted to the hands of the American people.” George Washington
Thomas Jefferson, Third President of the United States
“We act not for ourselves but for the whole human race. The event of our experiment is to show whether man can be trusted with self – government.” Thomas Jefferson
Theodore Roosevelt, 26th President of the United States
“The first requisite of a good citizen in this Republic of ours is that he shall be able and willing to pull his weight – that he shall not be a mere passenger.” Theodore Roosevelt
Abraham Lincoln, 16th President of the United States
“I leave you hoping that the lamp of liberty will burn in your bosoms until there shall no longer be a doubt that all men are created free and equal.” Abraham Lincoln
Trump: “Nobody likes me.“