The Washington Post this week reported, not only that the president is under investigation for possible obstruction of justice, but also that the FBI inquiry is examining the business and financial dealings of the president's son-in-law Jared Kushner.
Trump fired FBI Director James Comey in May, and that firing is now reportedly part of an investigation into whether Trump obstructed justice as president.
He also tweeted: "You are witnessing the single greatest WITCH HUNT in American political history - led by some very bad and conflicted people!"
Comey, who had been overseeing the bureau's Russian Federation investigation, says he had previously assured Trump he was not personally under investigation.
Comey was later sacked, with Trump acknowledging that the Russian investigation was on his mind when he made a decision to dismiss him. A day later, Rosenstein appointed Mueller as special counsel.
If Trump is found guilty of obstruction of justice, that would likely be grounds for impeachment.
Deputy Attorney General Rod Rosenstein has privately indicated that he may need to recuse himself from the probe into Russia's influence on the 2016 United States election, which would make him the second top tier law enforcement official to do so.
It was not immediately clear what prompted the release of that statement by Rosenstein, whether it was in response to recent stories that suggested the President was under investigation for obstruction of justice, or some other reason.
At a Senate Intelligence Committee hearing last week, Coats and Rogers refused to answer whether Trump asked them to intervene in the investigation.
While not denying the report, Marc Corallo, a spokesman for Trump lawyer Marc Kasowitz, called the Federal Bureau of Investigation leak of this information "outrageous, inexcusable and illegal". The NSA said in a statement that it will "fully cooperate with the special counsel" and declined to comment further.