The attorney general was at a White House meeting when the notification came from Rosenstein, prompting the enraged President to scold the attorney general for the turn of events.
Yet Trump's angry tweets on Friday underscored the near-impossible challenge his advisers and legal team have in trying to get him to avoid weighing in on an active investigation.
The president didn't clarify what exactly he was referring to in the early morning tweet, however he has frequently described reports about possible ties between members of his campaign and Russian Federation as a "witch hunt".
The Post reported that the interviews represent a widening of the probe to include looking into whether the President obstructed justice in suggesting to his former FBI Director James Comey that Comey drop the investigation into Michael Flynn, Trump's former national security adviser, as well as for his firing of Comey.
"Americans should be skeptical about anonymous allegations", Rosenstein said.
The department would not comment on the record on whether Trump, who has repeatedly complained about leaks on the case, requested the statement. Pence has hired Richard Cullen, a lawyer known for defending government officials in high-profile investigations, his office said on Thursday.
The interest in Kushner's activities by the special counsel's office is no more extensive than the FBI's interest in his multiple roles on both the Trump campaign and transition team, which CNN reported last month. 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. The White House used the memo to justify Comey's firing.More news: Russia Putin: Navalny urges people to join anti-corruption protests
"If the president is innocent, why is he afraid of this investigation?" asked NBC's Chuck Todd in a Meet the Press interview.
Citing unnamed sources, ABC reported Rosenstein told Associate Attorney General Rachel Brand she would have authority over the probe if he were to step aside. They are expected to work on setting formal terms of how the Hill and federal investigations will co-exist and share information - a major test on that front will be whether the FBI is willing to release Comey's memos of his conversations with Trump, now that they have been provided to Mueller.
Mr Mueller was appointed special counsel to investigate Russian involvement in the 2016 presidential election and possible collusion by Mr Trump campaign associates with the Russians, but there has been no indication that Mr Mueller told Mr Trump to fire Mr Comey.
A request to Trump campaign officials to preserve certain documents has revealed the scope of the ongoing investigation into the team's potential ties to Russian Federation.
On Thursday afternoon, Trump sent two tweets attacking his former opponent.
During his testimony before the same Senate committee last week, Comey said he felt he was sacked in large part because he refused to drop an Federal Bureau of Investigation probe into possible nefarious ties between Russian officials and Trump's campaign adviser and first national-security adviser, Michael Flynn.
Aides repeatedly deflected questions about the probe and Vice-President Mike Pence acknowledged hiring a private lawyer to handle fallout from investigations into Russian election meddling. These reports point to an important twist: Trump is now the subject of a criminal investigation because of actions he took as president.