Rosenstein may be a witness in the probe regarding the firing of former FBI Director James Comey.
President Donald Trump complained in a furious Friday morning tweet that he was being investigated for firing former FBI Director James Comey and seemed to accuse the deputy attorney general of overseeing a "witch hunt" against him.
Rosenstein released a cryptic statement the evening before about the danger of relying on anonymous sources, though it appeared to be aimed more at a report that the business interests of Trump's son-in-law and senior adviser Jared Kushner were now of interest to Mueller.
Days after Comey was abruptly ousted, Rosenstein appointed Robert Mueller as special counsel to investigate Russian involvement in the 2016 presidential election and possible collusion with the Trump campaign.
In a series of statements on Twitter on Thursday, Mr Trump repeated his claim that Mr Mueller's investigation is a "WITCH HUNT" based on the "phony" premise of possible collusion between Russian Federation and a cadre of Trump campaign associates.More news: Dozens killed, wounded in attack on Afghanistan police headquarters
During congressional testimony last week, Comey stated under oath the President was not under investigation by the FBI prior to or after his firing.
The White House confirmed Mr Mueller was among the candidates the president interviewed to replace Mr Comey.
Trump's Twitter response followed days of intensifying criticism of Mueller from some conservatives who have charged the former Federal Bureau of Investigation director and his team with political bias and have claimed his relationship to Comey and an earlier meeting with Trump amount to conflicts of interest.
The transition official spoke on condition of anonymity because the person was not authorized to discuss post-election decisions publicly. Jake [Tapper], Roger Stone, the president's longtime friend and associate told CNN Money earlier today this, "I'd fire Mueller and Rosenstein for wasting the taxpayer's money". An official of Trump's transition confirmed the laywer's internal order sent Thursday.
His aides try to change the subject when the president brings up Russian Federation, and aides have tried to reassure him the probe will clear him of wrongdoing - but he remains obsessed by what he believes is unfair treatment. Though some in the White House have preached caution, fearing a repeat of the firestorm over Comey's firing, many in Trump's orbit - including his son Donald Trump Jr. and adviser Newt Gingrich - have deemed Mueller biased and worthy of dismissal.More news: Saudi-Turkish ties strained over differing views on Qatar
The Post reports the other members include: 'former national security adviser Michael Flynn, former campaign chairman Paul Manafort and Carter Page, who was listed as a foreign-policy adviser for the campaign'.
As the legal rope has tightened, Trump's allies have gone on the offensive, questioning Mueller's credibility and floating the idea he may be fired. The transition team was led by Vice President Mike Pence.
Mr. Mueller's investigation appeared to be reaching a circle of current and former officials.
Trump's tweet is problematic on its own terms.
Comey said he typed notes describing the conversations because he was anxious Trump "might lie" later about them.More news: Trump tweet appears to confirm investigation
He had likened the appointment of the special counsel with the "single greatest witch hunt of a politician in American history".