(CNN) President Donald Trump has been eyeing potential replacements for several senior positions in his administration -- both inside the West Wing and across the Cabinet, multiple officials familiar with the matter said.

With the exception of his family working inside the White House, few aides feel completely secure as he considers a major shakeup, the officials said.

Kirstjen Nielsen, his secretary of the Department of Homeland Security, is potentially the next to go, multiple officials with knowledge of the matter said. Her departure could portend another high-profile exit: chief of staff John Kelly, Nielsen's top advocate in the administration.

Trump could ask Nielsen to resign in the coming days, multiple officials familiar with the matter predicted, describing the President's continued frustration at her handling of his signature issue: immigration and border security.

Meanwhile, Kelly is also on the list of possible resignations, despite Trump saying earlier this year he is welcome to stay in the post until the end of the President's term. Trump has been discussing a handful of replacements, including Nick Ayers, Vice President Mike Pence's chief of staff. The President had a long conversation with him on midterm election night last week, and has grown to like him, two officials said, but they cautioned it is far from certain whether Trump will dismiss Kelly and elevate Ayers.

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