The newspaper noted Mueller had requested interviews with CIA Director Dan Coats, National Security Agency chief Michael Rogers and Richard Ledgett, the former NSA deputy director.
Coats met behind closed doors for more than three hours Thursday with the Senate intelligence committee, which is conducting a separate investigation into Russian interference in the 2016 election.
Mueller has been building a team of investigators for a wide-ranging inquiry into Russia's meddling in the 2016 USA presidential campaign and whether any associates of President Donald Trump colluded in that effort.
"Trump had received private assurances from then-FBI director James Comey starting in January that he was not personally under investigation".
The White House referred all questions regarding the investigation to Trump's personal lawyer, Marc Kasowitz, who criticised the Post's report.
"The FBI leak of information regarding the President is outrageous, inexcusable and illegal", Corallo told CNN. The DNI's office and Ledgett declined to comment.
The NSA said in a statement: "NSA will fully cooperate with the special counsel. We are not in a position to comment further".
A spokesman for Mueller's team declined comment.
Probes launched as search continues for London fire victims
Theresa May has ordered a public inquiry into the Grenfell Tower blaze as more than a hundred residents are feared dead. Prime Minister Theresa May's office said she was "deeply saddened by the tragic loss of life" in the fire.
Trump took to his Twitter account Thursday morning to denounce the report.
Deputy Attorney General Rod Rosenstein, who appointed Mueller, hinted broadly that the special counsel investigation could be looking at Trump during a House committee hearing on Tuesday. The White House has denied any collusion, and Trump has repeatedly complained about the probe, saying Democrats can not accept his election win.Several congressional panels are also investigating the Russian Federation issue, which has cast a shadow over the early months of Trump's presidency.
Mueller has been tasked with leading the executive branch's investigation into Russian interference in the 2016 election and any potential collusion between Russia and Trump associates.
Senate Intelligence Chairman Richard Burr, a North Carolina Republican, and the panel's vice chairman, Mark Warner, a Virginia Democrat, said in a joint statement that the meeting was "constructive", but gave no details. "Nice", the president tweeted.
He said that is was "very strange" for Comey to relay the content of conversations with Trump and likened Comey to Edward Snowden, the former U.S. National Security Agency contractor who fled the United States after leaking details of extensive surveillance activities by U.S. intelligence and who has lived since 2013 in Russian Federation, where he has been granted asylum.
Coats and Rogers refused to comply with the president's requests, officials said.
"I took it as a very disturbing thing, very concerning, but that's a conclusion I'm sure the special counsel will work towards, to try and understand what the intention was there, and whether that's an offense", Comey testified last week.
The Washington Post first reported Wednesday that Mueller's probe was widening to include looking into whether Trump obstructed justice.
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