The White House confirmed that Mueller was among the candidates Trump interviewed to replace Comey. Chris Ruddy, the CEO of Newsmax and an ally of Trump, even floated the idea earlier this week that Trump was prepared to oust Mueller.
The Republican leader also lashed out at the Justice Department's number two, the man tasked with organising the probe.
President Trump confirmed Friday that he is under investigation for firing FBI Director James Comey. That ended the moment President Trump began tweeting about the special counsel's investigation into Russian meddling in the election and reportedly into the president himself.
Trump advisers and confidants describe the president as increasingly angry over the Russian Federation investigation, yelling at television sets in the White House carrying coverage and insisting he is the target of a conspiracy to discredit - and potentially end - his presidency. In that case, Rosenstein could be called as a witness.
Trump has been insisting that he is the target of a conspiracy to discredit and possibly end his presidency, according to the report.
The President's tweet sparked immediate speculation about the future of the official, Rod Rosenstein, who wrote a memo recommending Comey be ousted and also later approved the appointment of a special counsel - Robert Mueller - to lead the Russian Federation probe.
You don't have to be a Trump partisan to have concerns about where all of this headed. And it's up to him to decide how much to tell Rosenstein about the substance of the investigation itself.
Feinstein added, "That's undemocratic on its face and a blatant violation of the president's oath of office".
Aides have counseled the president to stay off Twitter and focus on other aspects of his job.
In another indication of the seriousness of the probe, Michael Cohen, a personal attorney to Trump, said he has retained attorney Stephen Ryan, a former assistant USA attorney, to represent him in the ongoing probes. "Nice", Trump wrote in his first tweet.
From 2011 until her confirmation, she was a lawyer for the US Chamber of Commerce business lobbying group's legal arm, which played a major role in marshaling legal opposition to environmental and labor regulations championed by Democratic former President Barack Obama.
The tweets came shortly after Rosenstein issued his unusual statement that appeared to be warning about the accuracy of such reports.
"Americans should be sceptical about anonymous allegations".
There is wide consensus that Trump is not doing himself any legal favors by repeatedly referring to it on Twitter.
Jack Goldsmith, a Harvard University law professor and a senior Justice Department official in the George W. Bush administration, immediately tweeted, "And the Deputy Attorney General should have better judgment". What is clear is that he could order the Justice Department to ax Mueller, which may result in Rosenstein's departure and would certainly intensify the uproar over the investigation. He testified that he leaked information about the notes through a friend to the Times to increase pressure for the appointment of a special prosecutor after he concluded Trump's administration "defamed" him and the Federal Bureau of Investigation after his May 9 firing.
ABC said Rosenstein told Associate Attorney General Rachel Brand she would have authority over the probe if he were to step aside.
During the Senate hearing, Comey said he made the memos because he thought Trump might lie about their interactions. Mueller may want to learn about Trump's conversations with Rosenstein, the Justice Department official who wrote the memo criticizing Comey's performance before his firing on May 9.