Donald Trump. Scott Olson/Getty Images

President Trump appears increasingly angry with Deputy Attorney General Rod Rosenstein — and experts say a resignation or firing could be coming next.

The president's feelings seemed to boil over in a Friday-morning tweet, possibly aimed at Rosenstein, in which Trump seemed to admit that he is under investigation, a claim reported by The Washington Post earlier this week.

The Post reported that special counsel Robert Mueller's investigation into Russian interference in the 2016 election has expanded to include a probe into whether Trump committed obstruction of justice with his firing of former FBI Director James Comey last month. Mueller is also investigating whether Trump associates committed financial crimes.

"I am being investigated for firing the FBI Director by the man who told me to fire the FBI Director!" Trump wrote. "Witch Hunt."

Rosenstein, who wrote a memo cited by Trump and Attorney General Jeff Sessions as the basis for Comey's firing, oversees Mueller, making the final calls about personnel, resources, and any prosecutions that would potentially arise from the investigation.

While it was not 100% clear that Trump meant Rosenstein when he wrote "the man who told me to fire the FBI Director" — the White House referred Business Insider to Trump's private legal team when asked who the president was referencing in his tweet — it came after a roughly week-long series of events that seemed to suggest the president was targeting the deputy attorney general, who hired Mueller as special counsel in mid-May following the firestorm that ensued from Trump's controversial firing of Comey. It was Comey's firing that proved to be the catalyst for the obstruction of justice probe.

But the timing of Trump's tweets seems strange.

On Thursday night, a day after the Post reported that Trump was under criminal investigation, and hours after Trump blasted what he called the "phony collusion with the Russians story" on Twitter, Rosenstein issued a curious statement suggesting that US citizens should "exercise caution before accepting as true any stories attributed to anonymous 'officials,' particularly when they do not identify the country – let alone the branch or agency of government – with which the alleged sources supposedly are affiliated."

"Americans should be skeptical about anonymous allegations," Rosenstein added. "The Department of Justice has a long-established policy to neither confirm nor deny such allegations."

Robert Chesney, a University of Texas law professor and cofounder of the Lawfare blog, told Business Insider in an email that the timing of Trump's tweet "apparently (though not all that clearly)" attacking Rosenstein is a head-scratcher.

It "is especially odd given that Rosenstein himself just last night issued a very uncharacteristic, Trump-friendly, statement attacking the media by implying that reporters have been disguising foreign government sources as US government sources," he said.

The statement came amid reports that Trump is both growing increasingly agitated by the special counsel probe and has considered firing Mueller. Comments from Trump confidant and Newsmax CEO Chris Ruddy and a New York Times story on Trump reportedly considering ousting Mueller apparently led officials to leak to the Post that the investigation included probing possible obstruction of justice. These stories would make it more difficult for Trump to remove Mueller without increased backlash.

Rod Rosenstein. Thomson Reuters

During testimony before the House and Senate appropriations committees Tuesday, a day after Ruddy told PBS "NewsHour" that Trump was considering firing Mueller, Rosenstein assured the committee that he would not do so unless he saw good cause, adding that he is "confident" Mueller "has full independence" to conduct the investigation. Rosenstein also said "there is no secret plan" to fire the special counsel "that involves me."

Just after Trump's Friday tweet, ABC News reported that Rosenstein has privately told his colleagues that he's considering recusing himself from the investigation, according to sources. Rosenstein oversees the special counsel since Sessions recused himself in early March from any matters involving the Trump campaign. If he were to recuse himself, Associate Attorney General Rachel Brand, third in command at the DOJ, would be next in line to oversee the special counsel.

Sources told ABC News that Rosenstein discussed his possible recusal in a recent meeting with Brand. Rosenstein told Brand that she would take over if he were to recuse himself from the matter.

A Department of Justice spokesperson told CNN that the deputy attorney general will recuse himself "if there comes a point where to needs to."

"However, nothing has changed," the spokesperson added.

Additionally, one of the main points of contention between Trump and Rosenstein, aside from Rosenstein's appointment of Mueller, is the memorandum Rosenstein wrote which was included in the rationale for firing Comey in May.

In his Friday tweet, Trump insisted that "the man who told me to fire" Comey is now investigating the president. In a private meeting with senators and representatives last month, Rosenstein said his memo was not a directive to fire Comey. But Rosenstein, in that same meeting, did defend the memo and the reasons he listed for why the FBI could benefit from new leadership. Comey's firing was recommended by Sessions, who cited Rosenstein's recommendation letter.

"On May 8, I learned that President Trump intended to remove Director Comey and sought my advice and input," Rosenstein said in the meeting. "Notwithstanding my personal affection for Director Comey, I thought it was appropriate to seek a new leader. ... "I wrote a brief memorandum to" Sessions "summarizing my longstanding concerns about Director Comey’s public statements concerning the Secretary [Hillary] Clinton email investigation. I chose the issues to include in my memorandum."

During an interview with NBC News' Lester Holt shortly after firing Comey, Trump said it was his "decision" to fire Comey and he would have done it "regardless of recommendation."

He made a recommendation," Trump said of Rosenstein. "He's highly respected. Very good guy, very smart guy. And the Democrats like him. The Republicans like him. He had made a recommendation. But regardless of recommendation, I was going to fire Comey knowing there was no good time to do it. And in fact, when I decided to just do it, I said to myself — I said, you know, this Russia thing with Trump and Russia is a made-up story. It's an excuse by the Democrats for having lost an election that they should've won."

Chesney said the Friday Twitter episode is adding to the already-strong speculation that Trump is going to try and fire Mueller. The easiest way for him to do so — what Chesney called the "front door" way — would be to simply ask Rosenstein to do so and have him comply.

But "tweets like this of course make it even less likely Rosenstein would comply," he said.

U.S. President Donald Trump signs an executive order at the White House in Washington, U.S. June 15, 2017. REUTERS/Eric Thayer

If Trump fired Rosenstein, and Brand became the one overseeing Mueller, Chesney said he'd find it highly unlikely she'd comply as well. That of course, Chesney said, could then lead Trump to fire her as well.

"But Trump might also try to avoid a confrontation with Rosenstein and Brand by instead going the 'nuclear' route: attempting to directly abolish the Office of Special Counsel altogether," Chesney said.

Andrew Wright, former associate counsel to President Barack Obama and Vice President Al Gore, told Business Insider that Trump's Friday tweet doesn't have a huge impact on the legal situation, but it does add to the "downward spiral on the political environment" where the investigations — both those in and out of Congress — are taking place.

"He is boxing himself into a corner ... by criticizing these folks without cause," Wright, now a professor at Savannah Law School, said. "He's making it much more politically difficult for natural allies in Congress to support the decisions he makes."

Wright said leaders in the DOJ and the White House counsel should be explaining to Trump why such attacks are not a good thing.

"Someone's got to be protecting the Department of Justice from that type of interference," he said. "Wildly inappropriate for the president to be commenting publicly and attacking officials at the Department of Justice who are trying to administer criminal laws."

While word of a possible Rosenstein recusal from the matter went public Friday, Wright said the deputy attorney general's "resignation is a real serious possibility here."

But "if you're Rosenstein, you have a real obligation to stay and take the heat," he added. And "be in a shock absorber role."

Democratic Sen. Dianne Feinstein of California — a top member on the Senate Judiciary and Intelligence committees — said after Trump's tweet that she's "growing increasingly concerned" that Trump will attempt to fire both Mueller and Rosenstein following Trump's Friday tweet.

"The message the president is sending through his tweets is that he believes the rule of law doesn’t apply to him and that anyone who thinks otherwise will be fired," she said in a statement. "That’s undemocratic on its face and a blatant violation of the president’s oath of office."

She said that Trump has "no authority" to fire Mueller, instead pointing to Rosenstein as the official whom holds that power. That could change, however, if Trump is able to rescind the special counsel regulation.

The other path would be firing Rosenstein and replacing him with another official who will "shut down the investigation," as Feinstein said. The California Democrat said Trump is "in for a rude awakening" if he thinks he can go about removing Mueller in that fashion.

"Even his staunchest supporters will balk at such a blatant effort to subvert the law," she said. "It's becoming clear to me that the president has embarked on an effort to undermine anyone with the ability to bring any misdeeds to light, be that Congress, the media or the Justice Department. The Senate should not let that happen. We're a nation of laws that apply equally to everyone, a lesson the president would be wise to learn."