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.

Ayers is not traveling with the vice president in Asia this week.

In recent weeks, the President has resumed polling advisers on potential replacements, as he did several months ago before ultimately announcing that Kelly would remain on as his chief of staff through his 2020 re-election campaign.

Ayers has told at least two friends he is in the running for the position, but it's unclear whether he knows his true standing in the volatile West Wing. He has grown close to the President and key members of the administration, including the President's daughter, Ivanka Trump, and son-in-law, Jared Kushner, and is valued for his political acumen -- something Trump allies have long grumbled that Kelly lacks.

One Republican close to the White House questioned how serious Ayers was under consideration. Other top aides, such as adviser Johnny DeStefano and budget director Mick Mulvaney, are also being discussed -- as well as others outside the administration.

DeStefano has presided over a growing portfolio inside a White House known for its complicated internal dynamics. He started out overseeing of the Office of Presidential Personnel, and has since been placed in charge of the political shop and the Office of Public Liaison.

A source close to Mulvaney said he is no longer interested in the chief of staff position. He is now far more interested in a Cabinet position as a next move, the source said.

Some Trump allies are urging the President to bring someone in from the outside, but it's an open question how attractive the position would be.

Trump hints at change

Speaking at his post-midterms news conference last week, the President made clear he was planning to shake up his staff, though declined to offer details.

"As we make changes, we'll sit down and talk to you about it. I mean, there's no great secret," he said. "A lot of administrations make changes after midterms. I will say that, for the most part, I'm very, very happy with this Cabinet. We're doing a great job."

Trump said he hadn't "heard about John Kelly" departing, but acknowledged any job at the White House is tiring.

"People leave. They come in, they're here. It's a very exhausting job," he said. "I love doing it, I must tell you. But it's exhausting for a lot of people."

The Washington Post reported Monday that Trump has told advisers he has decided to remove Nielsen and that he wants her out as soon as possible, citing five current and former White House officials.

Trump has vented privately that Nielsen hasn't adequately secured the border or enacted stricter immigration rules, even as she became the face of policies that administration critics called heartless and illegal, according to people familiar with the matter.

Asked to comment, Tyler Houlton, a Department of Homeland Security spokesman, said Nielsen "is honored to lead the men and women of DHS and is committed to implementing the President's security-focused agenda to protect Americans from all threats and will continue to do so."

The White House did not immediately return CNN's request for comment.

Nielsen's pending departure

Nielsen's potential departure would come after a midterm election campaign in which Trump focused heavily on immigration, often overlooking economic matters in favor of false or fear-mongering language about a crisis at the southern border.

Nielsen, who served in President George W. Bush's administration, never overcame internal skepticism about her allegiance to Trump. She joined the administration as chief of staff to John Kelly, who was Trump's first Homeland Security secretary.

When Kelly moved to the West Wing as chief of staff, Nielsen followed, becoming a deputy chief of staff tasked with helping Kelly bring rigor to a freewheeling staff.

Nielsen is widely viewed as an acolyte of Kelly, the retired Marine general who has his own complicated relationship with the President. Kelly has staunchly defended Nielsen against criticism of her performance on immigration-related matters. He's also been forced to defend her to the President, who has expressed suspicion over the jobs she held in the Bush administration.

Trump has angrily aired his frustrations with Nielsen's handling of border security during contentious meetings at the White House, claiming she isn't up to the task of fulfilling the campaign promises he made to curb illegal immigration. That, in turn, has led to an internal dynamic where some officials have griped to the President about Nielsen's performance in order to gain favor with him.

The President has not sought to quell that dynamic, believing that pitting camps of aides against each other is a way to produce better results. But the constant arrows have led Nielsen to tell some associates that she is unhappy in her post.