The Washington Post on Wednesday reported that Mueller is investigating the Republican president for possible obstruction of justice.
Trump appeared to confirm Friday that he is under investigation for obstruction of justice and seemed to use a social media posting to criticize Deputy Attorney General Rod J. Rosenstein.
"Americans should exercise caution before accepting as true any stories attributed to anonymous 'officials, ' particularly when they do not identify the country - let alone the branch or agency of government - with which the alleged sources supposedly are affiliated", Rosenstein said in the statement, which was released by the Justice Department.
Former FBI head Robert Mueller was appointed as special counsel a day after a report stemming from the notes was published.
In an interview with NBC's Lester Holt on May 11, Trump said he was "going to fire [Comey] regardless of recommendation" from Rosenstein and Sessions. But Rosenstein, too, may ultimately have to hand off oversight given his role in Trump's decision to fire Comey.More news: Seven US navy crew missing after collision
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Mr Comey told a Senate panel last week he believed Mr Trump fired him to undermine the FBI's Russian Federation probe and testified that the President directed him in February to drop an investigation into former national security adviser Michael Flynn in relation to the Russian Federation matter.
Kushner, the adviser and son-in-law of President Donald Trump, met separately with the Russian ambassador to the USA and a Russian businessman in December - interactions that were already under scrutiny as part of the Federal Bureau of Investigation probe.
He also claimed that the person investigating him advised him to fire Comey, though it's unclear whom he was referring to.
The memo to former transition team members on Thursday also seeks specific information on five people, the Times reported, They include Paul Manafort, Trump's former campaign manager; Rick Gates, Manafort's business partner; Carter Page, a former foreign policy adviser; former national security adviser Michael Flynn; and Roger J. Stone Jr., an informal adviser to Mr. Trump.
Published reports have indicated that Mueller is looking into whether Trump tried to obstruct justice.
If Rosenstein recuses himself, Brand, a Trump appointee, would become the top Justice official overseeing Mueller's work. But Trump fired Comey for his handling of the Russian Federation investigation.
Trump has called The Washington Post report a "phony story" and a "WITCH HUNT".
The transition official said the organization has also separately asked the General Services Administration to preserve records from the Trump transition that were transferred to its facilities after the inauguration. He has already been subpoenaed by the House of Representatives intelligence committee.