Mueller has asked for documents on Trump's reasons for firing former national security advisor Michael Flynn and ex-director of the FBI James Comey, theNew York Times reported on Wednesday.
Justice Department spokesman Ian Prior reiterated Rosenstein's previous assertion that he would recuse himself from the Russian Federation investigation if necessary, but said that as of now, "nothing has changed". President Donald Trump described the investigation as a "witch hunt" after Mueller was appointed by the Justice Department to oversee the federal investigation into the allegations, giving him sweeping powers and the authority to prosecute any crimes uncovered in the probe.
Citing White House officials, The Times reports that Mueller is also interested in the circumstances surrounding the dismissal of Trump's first national security advisor, Michael Flynn; as well as an Oval Office meeting with Russian officials during which Trump said that the Comey firing relieved "great pressure" on him.
A special counsel can be removed by the attorney general or, if the AG has recused himself, the most senior Department of Justice official.
According to a summary of their meeting provided to The New York Times, Trump told Lavrov and Kislyak that Comey was "a nut job" and that firing him had eased the pressure of the Russian Federation investigation.More news: Trump Takes Aim at Venezuela in UN Speech
The White House initially explained Comey's firing by saying Trump was acting on the recommendation of Rosenstein, who wrote a scathing memo about Comey's handling of the Hillary Clinton e-mail investigation.
The lawyer handling the matter for the president Ty Cobb, told Mueller's office that he will turn over numerous documents this week, according to The Times.
Mueller also wants to know more about a meeting Trump had with the Russian foreign minister Sergey Lavrov and former Russian ambassador Sergey Kislyak in the Oval Office one day after firing former FBI Director James Comey, according to the Times.
Mueller's office sent a document to the White House seeking more information about 13 different areas, prompting administration lawyers to gather White House emails and ask officials if they have other documents or notes pertinent to Mueller's requests. "He was insane, a real nut job", Trump said, according to a document obtained by the Times at the time.
White House press secretary Sarah Huckabee Sanders told reporters last month that "the president weighed in" on the Trump Tower meeting "as any father would based on the limited information he had".