Trump is reportedly being investigated by the FBI for obstruction of justice
As part of the probe, Mueller is interviewing senior intelligence officials and looking for proof of any financial crimes possibly committed by Trump's associates, the Post reported, citing US officials.
A spokesman for Trump's lawyer said in a statement that "the FBI leak regarding the President is outrageous, inexcusable, and illegal," but did not dispute the accuracy of the report.
The scope of the probe had been previously limited to possible collusion between Russia and the Trump campaign. Former FBI Director James Comey confirmed in a Senate testimony last week that he had told Trump three times between January and March that he was not personally under investigation.
According to the Post, that changed just days after Trump fired Comey, who was leading an FBI investigation into Trump's campaign team and whether it colluded with the Kremlin during the 2016 election when he was fired on May 9.
Trump told two Russian diplomats in an Oval Office meeting just one day after firing Comey, that by dismissing the former FBI director - who he reportedly called a "nut job" - that he had taken "great pressure" off of himself, according to The New York Times. Days later, he told NBC's Lester Holt that "the Russia thing" had been on his mind when he fired Comey.
Those comments, combined with his alleged request to Comey in February that the FBI considering dropping its investigation into Michael Flynn, the former national security adviser, have led lawmakers, legal experts, and now Mueller to question whether Trump sought to obstruct justice, a criminal and impeachable offense.
Three intelligence officials could be interviewed by Mueller as early as next week: Director of National Intelligence Daniel Coats, National Security Agency chief Mike Rogers, head of the National Security Agency, and former NSA deputy Richard Ledgett, who retired in April.
Trump has reportedly considered firing Mueller, who he thinks is too close to Comey and is engaged in a "witch hunt" against him. But he has been advised it by his aides in recent days.