Washington (CNN) President Donald Trump's aides have explored moving some impeachment witnesses on loan to the White House from other agencies, such as Lt. Col. Alexander Vindman , back to their home departments ahead of schedule, according to people familiar with the conversations.

As public hearings bring the officials' allegations to his television screen, Trump is asking anew how witnesses such as Vindman and Ambassador Bill Taylor came to work for him, people familiar with the matter said. He has suggested again they be dismissed, even as advisers warn him firing them could be viewed as retaliation.

The possible move of officials out of the White House could still be viewed by some as evidence of retribution for their testimony. Trump's frustration at his own officials comes as he attacks witnesses on Twitter, including during Friday's public hearing with the ousted ambassador to Ukraine Marie Yovanovitch . Trump appears to have adopted a strategy of maligning the officials, despite some allies encouraging him not to.

The uncertain fate and public thrashing of these officials has created a thorny situation for a White House wading through the impeachment process. Trump's impulse to dismiss them hasn't been realized, but he's made clear nevertheless he views them as unwelcome.

It's one of the persistent anomalies of the impeachment inquiry: most of the witnesses airing concerns at Trump's approach to Ukraine remain employed by him, despite his claims they are "Never Trumpers" and his overt suggestions they've already been fired.

None, for now, have been explicitly fired by Trump, even as he and his allies suggest otherwise. It's created an odd and uncomfortable situation for staffers, who say they are unclear on their colleagues' futures in the administration.

Over the weekend, a GOP talking point emerged that Trump was well within his rights to choose his own team, a response to Yovanovitch public recounting of the smear campaign orchestrated by Trump's allies to push her from her post in Kiev.

"America hired @realDonaldTrump to fire people like the first three witnesses we've seen," the President's son, Donald Trump Jr., tweeted as Yovanovitch began her testimony. "Career government bureaucrats and nothing more."

A day later, Trump himself suggested on Twitter he'd already fired the three State Department employees who have appeared in public impeachment hearings, quoting the conservative radio host Rush Limbaugh.

"You elected Donald Trump to drain the Swamp, well, dismissing people like Yovanovitch is what that looks like. Dismissing people like Kent and Taylor, dismissing everybody involved from the Obama holdover days trying to undermine Trump, getting rid of those people, dismissing them, this is what it looks like," Trump tweeted, citing Limbaugh.

He was referring to George Kent , the current deputy assistant secretary of state for European and Eurasian affairs, and Bill Taylor, the current top US diplomat in Ukraine.

The message left the impression that Trump was fulfilling a campaign promise by removing those who'd testified about their concerns. But as of Monday, all three of the people named in his tweet remain employed by his administration. Kent and Taylor are still in their posts, and while Yovanovitch took a position at Georgetown University after being recalled, she remains a State Department employee.

Trump has not taken formal steps to order those officials' removal from government, according to administration officials, who say instead he has vented at how they were allowed to work for him in the first place. In the case of Taylor, Trump has lashed out at Secretary of State Mike Pompeo, who personally encouraged Taylor to come out of retirement when Yovanovitch was recalled.

Asked at a news conference Monday whether the President had confidence in Taylor, Pompeo demurred.

"The State Department is doing a fantastic job. I think we've delivered in a way that the Obama Administration has not delivered on Ukraine," Pompeo said, declining otherwise to state whether the top envoy in Ukraine was still in the President's good graces.

He did offer blanket support for his staff as they withstand attacks from the President and his allies.

"I always defend State Department employees. This is the greatest diplomatic corps in the history of the world. Very proud of the team," he said, without rebutting any of Trump's claims.

Warned against action

Early in the impeachment proceedings, as witnesses came to deliver closed depositions on Capitol Hill, Trump's advisers warned him against taking steps to fire those speaking out. His actions could be perceived as retaliation, they cautioned, and could be used by Democrats as they compiled articles of impeachment.

But now, the strength of that advice is being tested by televised hearings and the public release of the private interviews. Trump has watched the hearings intermittently and consumed hours of news coverage afterward.

On Sunday, Trump lashed out at another witness, Jennifer Williams, a State Department employee on loan to the vice president's office as a foreign policy adviser. On Twitter, the President wrote, "Tell Jennifer Williams, whoever that is, to read BOTH transcripts of the presidential calls, & see the just released ststement (sic) from Ukraine. Then she should meet with the other Never Trumpers, who I don't know & mostly never even heard of, & work out a better presidential attack!"

Asked about the tweet, Vice President Mike Pence's spokeswoman said only: "Jennifer is a State Department employee." The State Department didn't comment.

Despite Pence's office distancing themselves from Williams in public, White House sources said Williams still has the support of his team, including chief of staff Marc Short and Williams' boss, Gen. Keith Kellogg, who serves as Pence's national security adviser.

"She is just as key a part of the team," a White House official said.

For now, the expectation is that Williams, who was detailed to Pence's office from the State Department earlier this year, will remain in her post. However, there's "no chance" Pence will step forward to defend Williams, the official added.

"In the press it has been pretty clear that he is distancing himself from 'the deep state,' " the official said.

Vindman's fate

JUST WATCHED Lt. Col. Vindman explained why he thought Trump was making a 'demand' of Ukraine Replay More Videos ... MUST WATCH Lt. Col. Vindman explained why he thought Trump was making a 'demand' of Ukraine 03:59

Less clear is the fate of Vindman, who will appear in a public hearing on Tuesday morning alongside Williams. The top Ukraine expert on the National Security Council, Vindman raised concerns about Trump's July phone call with Ukraine's President to National Security Council lawyers.

Additional testimony from Tim Morrison, the council's former senior director for European and Russian, suggested internal concerns about Vindman's suitability for the job. Morrison said he was warned about Vindman's judgment from his predecessor, Fiona Hill.

Like many National Security Council staffers, Vindman is detailed to the agency from the Defense Department, where he served as a foreign area officer. His twin brother Lt. Col. Yevgeny Vindman is also assigned to the council as a lawyer, and accompanied Alexander Vindman when he brought his concerns to White House lawyers.

In the wake of his testimony, some officials at the White House have explored moving both men back to the Pentagon, according to people familiar with the matter. But it's not clear when that might occur. And Alexander Vindman's lawyer said recently his detail to the National Security Council does not expire until next summer.

Speaking on CBS earlier this month, national security adviser Robert O'Brien said Vindman would likely return to the Pentagon but framed the move as part of his larger efforts to reduce the size of the National Security Council.

"We're streamlining the National Security Council. There are people that are detailed from different departments and agencies. My understanding is that Colonel Vindman is detailed from the Department of Defense," he said. "So everyone who's detailed at the NSC, people are going to start going back to their own departments."

He didn't specify whether the move would occur earlier than planned, and insisted it did not amount to retaliation for Vindman's testimony.

"I never retaliated against anyone," O'Brien said.