The revelation that Mueller is investigating whether Trump tried to obstruct justice follows Comey's blockbuster testimony last week.
That would mean it began before Robert Mueller was appointed as special counsel by Deputy Attorney General Rod Rosenstein on May 17. The essence of Comey's testimony was that the president asked him to drop an investigation of retired Lt. Gen. Michael Flynn - Trump's former national security adviser - and then asked him to do so in return for keeping his job as FBI director and then fired him for not obeying his order.
The transition official spoke on condition of anonymity because the person was not authorized to discuss post-election decisions publicly.
Mark Corallo, a spokesman for Trump's legal team, on Wednesday denounced the report, saying: 'The FBI leak of information regarding the President is outrageous, inexcusable and illegal'.
On Wednesday night, a spokesman for Trump's lawyer did not refute the notion that Trump was under examination but decried what he said were leaks that the led to the story. "President Trump said prior that once he gets in he's going to kick the S-H-I-T out of the enemy".
The NSA told the paper it will 'fully cooperate with the special counsel, ' while the office of the Director of National Intelligence and Ledgett declined to comment.
Comey also testified he had told Trump he was not under investigation.
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Mr Comey confirmed in his testimony to the Senate intelligence committee last week that Mr Trump was not personally under investigation for contacts with Russian Federation, despite an ongoing probe into links between his campaign team and the Kremlin.
Quoting officials, the Post said one event of interest to Mueller, a widely-respected former head of the Federal Bureau of Investigation is an exchange on March 22, when Coats told associates Trump had asked him to intervene with Comey to get him to back off from focusing on Flynn.
Trump ignored shouted questions from reporters about the ongoing Russian Federation controversy as he departed the White House Friday for Miami. Rosenstein told The Associated Press this month he would recuse himself from any oversight of Mueller if he were to become a subject of the probe.
Some Trump allies outside of his administration, including former House Speaker Newt Gingrich, have either suggested Mueller can not be independent or called for his ouster.
The leaders of the Senate Intelligence committee said in a statement issued Wednesday that they "look forward to future engagements" with Robert Mueller.
"I don't think it's for me to say whether the conversation I had with the President was an effort to obstruct", Comey said.
Comey testified before the Senate Intelligence Committee last week that he was certain his firing was due to the president's concerns about the Russian Federation probe, rather than over his handling of a now-closed FBI investigation into Hillary Clinton's use of a private email server as secretary of state, as the White House had initially asserted.