WEST DES MOINES, Iowa—For those who speculate about what Vivek Ramaswamy really wants out of his long-shot Republican presidential bid—perhaps a podcast or a television contract—the wealthy biotech entrepreneur has one answer.

“I expect to be the president,” he said in an interview as he crisscrossed this state ahead of the presidential caucuses Monday that will start the 2024 nomination balloting. But that expectation rests on hopes for a dramatic change in the race: Donald Trump’s departure.