Mr Trump did not identify who "the man" was but appeared to be questioning the integrity of Deputy Attorney-General Rod Rosenstein - the Justice Department's number two official who appointed Mr Mueller on May 17 and wrote a memo to Mr Trump that was critical of Mr Comey's performance after the former director was sacked.
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 led to the story.
Trump did not make it clear whom his tweet was referring to.
They say senior intelligence officials will be interviewed about whether Mr Trump tried to end an inquiry into his sacked national security adviser.
Mr Trump is an avid user of Twitter, with more than 32 million followers on his personal account and over 18 million on the official presidential account.
Coats and Rogers refused to answer questions about the matter during a Senate committee hearing last week.
Reuters cited a source which confirmed the Post report, adding that an examination of possible obstruction of justice charges was "unavoidable" after former FBI Director James Comey told Congress he believed he was sacked by Trump to undermine the agency's Russian Federation investigation.
While accusing the Clinton campaign and the Obama administration of indulging in illegal acts, Trump had said that "there was never a special counsel appointed to oversee the acts of his Democrat predecessors".
Trump earlier derided claims of collusion between Moscow and his associates as "phony" Thursday after reports the head of a probe into Russia's alleged election meddling is investigating him for obstructing justice.