But Rosenstein could end up recusing himself, too, Justice officials say, in part because he played a role in President Donald Trump's firing of FBI Director James Comey.
In an editorial written for the Washington Post, Starr tells Trump that it would be an "insult to the Founding Fathers" if he fired the man who is leading an investigation into him and his presidential campaign.
- One of President Donald Trump's personal lawyers said in television interviews on Sunday that the President was not under investigation for obstruction of justice, but when pressed on the assertion, said he was not certain.
Trump did not specify who he was referring to, but he appeared to be questioning the integrity of Deputy Attorney General Rod Rosenstein, the US Justice Department's No. 2 official.
The President's tweet - seeming to confirm the probe based on news reports - came as a surprise to the President's own legal team, according to a person briefed on the matter.
The president has said he already made his decision to fire Comey before Rosenstein wrote a memo criticizing the director's handling of the Hillary Clinton email investigation.
A person familiar with Mueller's inquiry, speaking on condition of anonymity, said on Thursday Mueller was looking into whether Trump or others attempted to obstruct the Russian Federation investigation. Trump said last week he felt vindicated by Comey's June 8 testimony that he was not the subject of investigation while Comey headed the agency.
Rosenstein has said privately he may need to recuse himself from matters relating to the Russian Federation probe because he could become a witness in the investigation, ABC News reported on Friday.
Barak Cohen, a former Justice Department lawyer and now a defense attorney specializing in white-collar crime and investigations, said there was no requirement that the special counsel notify Trump he was under investigation, so the lack of such notice meant nothing.
Sen. Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, said she was "increasingly concerned" that Trump will fire both Mueller and Rosenstein.
Rosenstein also has authority to fire Mueller, if he finds evidence of good cause. By that afternoon, Trump was re-litigating the 2016 election; "Why is that Hillary Clintons family and Dems dealings with Russian Federation are not looked at, but my non-dealings are? he tweeted". The American people deserve to know just how deeply Moscow delved into our election process - and whether any Americans were connected to the interference with our democratic process.
What do you think of the current turn of events in the White House?
Trump kept up his criticism of the investigations in a series of tweets on Friday. "Sad!" he wrote in one post.
"I would give him the chance to see if he could do that because if there's nothing there, he's not going to find anything anyway", Carson said.
The order from the general counsel for the transition team casts a wide net on documents that could shed light on ties between Trump's presidential campaign and representatives of Russia's government.
The memo to former transition team members on Thursday also seeks specific information on five people, the Times reported. The order also covers separate inquiries into several key Trump associates including Flynn; campaign adviser Paul Manafort and his business partner, Rick Gates; foreign-policy aide Carter Page; and outside adviser Roger Stone. Rosenstein also insisted Mueller's investigation would have the resources it needs.