In characteristic style Mr Trump himself struck back on Twitter.
The investigation into ties between President Trump's campaign and the Russian government has now turned to investigating Trump himself for obstruction of justice, the Washington Post reported Wednesday.
A Trump confidant this week said, for example, the president has "considered" firing Mueller.
President Trump on Thursday criticized reports that he is now under investigation for obstruction of justice in connection with the firing of FBI Director James Comey, denouncing it as another "witch hunt" that is unfairly targeting him.
A spokesman for Mr Mueller's team declined to comment on Wednesday. The investigation has been cloaked in secrecy, and it is unclear how many others have been questioned by the FBI. After Comey's testimony, Trump called him a liar and suggested he would testify to his version of events under oath - a disastrous strategy.
President Trump, appearing before the cameras on his 71st birthday, speaks about the shooting of five people at a Republican baseball practice on June 14, 2017.
Comey testified last week that he also felt pressured to drop the Flynn probe.
According to Jarrett, the special counsel statute says, if you have a personal relationship with someone substantially involved in the case you shall not serve as special counsel.
Wall Street flat as banks fall after weak data; Fed eyed
Declining issues outnumbered advancing ones on the NYSE by a 1.13-to-1 ratio; on Nasdaq, a 1.41-to-1 ratio favored decliners. Investors will also be looking for any details on the Fed's plans to trim its $4.5 trillion balance sheet.
Blimp goes down at US Open
I used to not be a very good bunker player, and now I feel like I have a lot of confidence, and stats show I'm one of the best. Open defence, courtesy of Curtis Strange in 1989, and Dustin Johnson has much work to do if he is to buck that trend.
Ken Starr: Not Enough Evidence for Trump Obstruction Case
In a pair of earlier tweets, Trump called the investigation "phony" and the "greatest WITCH HUNT in American political history". The probe into Trump was sparked in part by the sudden dismissal of FBI Director James Comey .
"The FBI leak of information regarding the president is outrageous, inexcusable and illegal", said spokesman Mark Corallo.
Mueller met Wednesday with the leaders of the Senate Intelligence Committee in an effort to ensure their investigations don't conflict.
"That means it wasn't Robert Mueller's decision personally to launch this investigation into the president - it would have been started before him, is that right?"
"When I chose to just do it [fire Mr. Comey], I said to myself, you know, this Russia thing with Trump and Russia is a made-up story", Mr. Trump casually explained to NBC's Lester Holt, a few days after he allegedly told Russian officials that Mr. Comey was canned for being a "nut job" and that he was happy the "pressure because of Russia" was now gone.
The ascendancy of Mr. Trump has been an ongoing reminder that laws are only as good as the people who uphold them.
There's no guarantee that the office of the special counsel will pursue this line of investigation, says Entous - these meetings are merely the first step to help investigators determine whether there's more evidence to uncover about obstruction of justice.
Quoting officials, the newspaper said one event of interest to Mueller is an exchange on March 22, when Coats told associates that Trump had asked him to intervene with Comey to get him to back off the focus on Trump's former national security advisor Mike Flynn as part of the Federal Bureau of Investigation probe of the Russian Federation affair.
Rep. Adam Schiff, the top Democrat on the House Intelligence committee, said such a move would "be the last straw" for many in Congress and would have "echoes of Watergate", when President Richard Nixon dismissed special prosecutor Archibald Cox over Cox's subpoenas for White House tapes.