Senior intelligence officials will be interviewed on whether President Trump tried to end an inquiry into his sacked national security adviser, and about the firing of FBI chief James Comey.
Donald Trump’s legal team said the latest leak to the media was “outrageous”.
Robert Mueller is leading an FBI inquiry into Russian meddling in the election.
Donald Trump has repeatedly denied any collusion with Russia, describing the ongoing inquiry as a “witch hunt”.
The latest development was first carried in the Washington Post. Later the New York Times and Wall St Journal reported the story, citing their own sources.
The Washington Post said the decision by Robert Mueller to investigate President Trump’s own conduct is a major turning point in the investigation, which until recently focused on the Russian angle.
The latest media reports say the obstruction of justice investigation began just days after Donald Trump fired James Comey on May 9.
James Comey, who had been leading one of several Russia inquiries, testified to Congress last week that President Trump had pressured him to drop the investigation into former National Security Adviser Michael Flynn.
Mike Flynn was sacked in February for failing to reveal the extent of his contacts with Russian ambassador to Washington, Sergei Kislyak.
James Comey testified under oath that President Trump had told him during a private meeting: “I hope you can see your way clear to letting this go, to letting Flynn go. He is a good guy. I hope you can let this go.”
The White House has said President Trump “has never asked Mr. Comey or anyone else to end any investigation, including any investigation involving General Flynn”.
James Comey had testified he was “sure” Robert Mueller was looking at whether Donald Trump had obstructed justice.
However, James Comey also testified that, to his knowledge, President Trump had not tried to stop the Russia investigation.
Meanwhile, the Wall St Journal quoted a source as saying that Robert Mueller would examine whether James Comey’s sacking was an attempt by the president to alter the course of the investigation.
President Trump said he had fired James Comey because of the “Russia thing”.
He reportedly told Russian officials at an Oval Office meeting a day after sacking Director James Comey that his position had now eased.
“I faced great pressure because of Russia. That’s taken off,” Donald Trump said, according to a US official quoted by the New York Times.
The latest reports also speak of an investigation into possible money laundering among Trump associates.
A former senior official told the New York Times that any collusion between the Trump team and Russian officials would have involved a pay-off, and that there may have been attempts to hide the route of the payments by using offshore banking.
The three names being mentioned in media are Daniel Coats, the director of national intelligence, Mike Rogers, the head of the National Security Agency, and Richard Ledgett, until recently Admiral Rogers’ deputy.
At a Senate panel last week, Daniel Coats and Mike Rogers declined to answer questions about conversations with the president, but said that they had never felt pressured to interfere in investigations.
The Washington Post says the three have agreed to be interviewed by investigators and the questioning could happen as early as this week.
The three were not involved in the Trump campaign but may be asked whether President Trump sought their help to end the Flynn inquiry.
A separate Washington Post report has said that Daniel Coats told associates in March that the president had asked him to try to get the FBI to back off.
However, the Times points out that the latest questioning does not mean a criminal case is being built against President Trump, simply that information is being gathered by the FBI. It will be passed to prosecutors who will then have to decide.
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