Rosenstein wrote the memo laying out the case for new leadership at the Federal Bureau of Investigation.
The Justice Department did not immediately respond to CNBC's request for comment. But Rosenstein is not now heading the FBI's probe into the Trump campaign's possible collusion with a Russian campaign that USA intelligence officials have said was seeking to tilt the outcome of the 2016 election in Trump's favor. Rosenstein finds himself in a spot as he could face the President anger or answer questions about his own future role supervising Mueller when he could become a witness in the special counsel's probe. Former FBI head Robert Mueller was appointed as special counsel a day after a report stemming from the notes was published.
At a Senate Intelligence Committee hearing last week, Coats and Rogers refused to say whether Trump asked them to intervene in the investigation, which is also examining whether the Trump campaign team colluded with Russian Federation during last year's presidential campaign.
The president complained the probe is unfair and wondered why his defeated Democratic opponent wasn't getting the same scrutiny.
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At a ceremony last month to welcome Associate Attorney General Rachel Brand, the Justice Department's third-ranking official, Rosenstein joked awkwardly about being at the center of criticism since taking office, according to people who were in the room.
Mueller's investigation appeared to be reaching a broadening circle of current and former officials.
Mr Trump was not under investigation before Mr Comey's firing, but reportedly is now facing scrutiny for obstruction of justice over the circumstances surrounding the ex-FBI chief's sacking, according to U.S. media.
Comey testified under oath to the Senate intelligence committee earlier in June that Trump told him in a private conversation: "I hope you can see your way clear to letting this go, to letting Flynn go".
The order from the general counsel for the transition team casts a wide net on documents that could shed light on ties between Mr Trump's presidential campaign and representatives of Russia's government.