President Trump is scheduled to interview at least four candidates for the national security advisor position in Florida on Sunday.
The meetings come after Trump's first choice to replace retired Gen. Michael Flynn, retired Vice Adm. Robert Harward, turned down the position.
Trump told reporters on Air Force One Saturday that he had "many, many that want the job."
He also suggested that he may already have a person in mind for the position.
"I've been thinking about someone for the last three or four days, we'll see what happens," Trump said. "I'm meeting with that person. They're all good, they're all great people."
According to Reuters, Trump told reporters that he plans to "make a decision over the next couple of days."
Scheduled to meet with the president at Mar-a-Lago include his acting adviser, retired Army Lt. Gen. Keith Kellogg; John Bolton, a former U.S. ambassador to the United Nations; Army Lt. Gen. H.R. McMaster; and the superintendent of the U.S. Military Academy at West Point, Lt. Gen. Robert Caslen.
White House spokesman Sean Spicer said there could be more meetings for the job, which unexpectedly opened after Flynn's firing early this week.
Flynn resigned at Trump's request Monday after revelations that he misled Vice President Mike Pence about discussing sanctions with Russia's ambassador to the U.S. during the transition.
Trump said Thursday that he was disappointed by how Flynn had treated Pence but did not believe Flynn had done anything wrong by having the conversations.
In his first post-inauguration rally on Saturday, Trump talked about his first month of the presidency and what plans he has ahead.
The president told supporters that he would deliver "change for the ages."
"You want a government who keeps its promises and a great optimism is sweeping, and you see it sweeping all across the country," he said. "Look at the stock market. Look at what is happening to every poll when it comes to optimism in our country."
He told the crowd how he would secure America's borders and strengthen the military.
"I have ordered the Department of Defense to begin plans for the great rebuilding of the United States' military," he said. "We will pursue peace through strength."
He also mentioned that he is working on a new healthcare plan that will replace Obamacare, once it is repealed.