Still, since Trump fired the former FBI director, James Comey, who was overseeing the Russian Federation probe little more than a month ago, the White House comments have stirred concern among members of Congress that Mueller might get the same treatment if the investigation goes against the president.
President Donald Trump took to Twitter early Friday morning to confirm that he is under investigation - or as he likes to call it, a "witch hunt".
Deputy Attorney-General Rod Rosenstein submitted a widely circulated memo to the President last month raising concerns over Mr. Comey's performance, but Mr. Trump later asserted that he had already made the decision himself to fire Mr. Comey.
Hours after Mr Trump's tweet, a source close to his outside legal team said the President did not intend his tweet to be confirmation of the investigation but rather was a reaction to a Washington Post story about the probe from Wednesday (local time).
Mueller is leading the Russian Federation probe after being appointed by Deputy Attorney General Rod Rosenstein in the Department of Justice, which oversees the Federal Bureau of Investigation.
Trump "believes that he has the power to fire anyone in government he chooses and for any reason", said Representative Adam Schiff, whose committee is also investigating Russia-Trump ties.
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The White House has said the president "has never asked Mr Comey or anyone else to end any investigation, including any investigation involving General Flynn". "Nice", Trump wrote on Twitter.
At a congresional hearing last week, Comey confirmed that he told Trump three times that Trump was not being investigated as part of the Russia-collusion probe, and Trump tweeted "total and complete vindication" at that time.
President Trump has repeatedly denied any collusion with Russian Federation, describing the ongoing inquiry as a "witch hunt".
In the most famous presidential investigation, Watergate, Archibald Cox was appointed special prosecutor on May 18, 1973 - by June 5, Nixon was complaining about being attacked by Cox.
While a sitting president is unlikely to face criminal prosecution, obstruction of justice could form the basis for impeachment. "#MAGA", Trump said in another tweet.
Mr Comey testified under oath that Mr Trump had told him during a private meeting: "I hope you can see your way clear to letting this go, to letting Flynn go".