White House aides approached South Dakota Gov. Kristi Noem last year about the process of adding additional presidents to Mount Rushmore, the NYT reported citing a Republican official familiar with the conversation. Noem, in a 2018 interview, had confirmed that during a conversation Trump told her that having his face on Mount Rushmore was his ’dream’.
If any additions are made to Mount Rushmore, it should be related to the Native American whose lands where violated for its construction.
This is missing some important info. From what I read, it wasn't his idea. That was misreported. Also while he did say it sounded like a good idea, he said it jokingly.