President Donald Trump speaks while meeting with Egyptian President Abdel Fattah el-Sisi in the Oval Office of the White House, Tuesday, April 9, 2019, in Washington.

President Donald Trump's ongoing leadership shake-up at the Department of Homeland Security is aimed squarely at the agency's "bureaucracy," a senior administration official said Tuesday, and not on lower level staffers.

"There's a lot of false rumors and assumptions out there about names of people in the agencies" who might be asked to leave their jobs, said the official, who declined to be named. "I want to be very clear in saying that we're not taking any look at any subordinate staffers."

By emphasizing that the jobs of lower level staffers were not in danger, however, the official left wide open the possibility that the White House is considering additional DHS changes at the leadership level, although they declined to say who might be asked to leave.

In the past five days, Trump has fired Homeland Security Secretary Kirstjen Nielsen, told U.S. Secret Service director Tex Alles to resign, and withdrawn his nomination of Ron Vitiello to lead U.S. Immigration and Customs Enforcement.

Several news outlets have also reported that Trump is considering replacements for the current director of U.S. Citizenship and Immigration Services, Francis Cissna, and John Mitnick, the Homeland Security Department's general counsel.

Trump denied on Tuesday that he was "cleaning house" at the department, saying lots of "good people" still work at DHS.

Likewise, the senior White House official said the departures from DHS were aimed at creating the right environment for a much-needed update to the department's approach to immigration policy, setting aside Obama-era practices and embracing Trump's more hardline policies.

"They haven't even updated their training materials from the Obama era," the official said. "People felt no urgency to make these policy changes the White House was pushing."