Mueller is interviewing senior intelligence officials about Trump's conduct in a new phase of the inquiry, which reportedly began soon after Trump fired FBI Director James Comey as the FBI was investigating ties between the president's associates and Russian Federation.
"What was Comey's involvement in having Mueller appointed to special counsel and is Mueller going to have to investigate Comey, who public reports suggest is either a friend or a protégé of Mr. Mueller?"
Former FBI Director James Comey testified last week that the president was not personally under investigation at the time of his firing on May 9.
In the interview, Mr Ruddy said Mr Trump had considered replacing Mr Comey with Mr Mueller, who served as Federal Bureau of Investigation director during the George W. Bush and Barack Obama administrations.
Shortly after Robert Mueller was named special counsel in the federal Russian Federation investigation, lawmakers speculated that the congressional probes may be sidelined by the forceful new presence.
Conservative commentator Ann Coulter offered a similar message, tweeting, "Now that we know TRUMP IS NOT UNDER INVESTIGATION, Sessions should take it back & fire Mueller".
Mueller spokesman Peter Carr told NPR's Carrie Johnson, "We'll decline to comment".
Focus Brexit on economy, Scottish Conservatives urge British PM
The Scottish Conservative leader arrived at Downing Street as SNP leader Nicola Sturgeon met her party's 35 MPs outside the Houses of Parliament.
Under current Justice Department regulations, firing Mueller would have to be done by Attorney General Jeff Sessions' deputy, Rosenstein, not the president- though those regulations could theoretically be set aside.
House Russia probe leader Michael Conaway, a Texas Republican, and Rep. Adam Schiff, the investigation's top Democrat, were set to meet with former Homeland Security Secretary Jeh Johnson - just a few days after Senate investigators interviewed him.
The White House wouldn't deny or confirm the report and said, "only the president or his attorneys are authorized to comment". Reporter Tony Mauro noted the addition of Dreeben may signal that "Mueller may be seeking advice on complex areas of criminal law, including what constitutes obstruction of justice". "I think there's a conflict there".
[B] ehind the scenes, the president soon began entertaining the idea of firing Mr. Mueller even as his staff tried to discourage him from something they believed would turn a bad situation into a catastrophe, according to several people with direct knowledge of Mr. Trump's interactions.
Accounts by Comey and other officials of their conversations with the president could become central pieces of evidence if Mueller decides to pursue an obstruction case. "I don't question his integrity at all, but he has to be careful not to create the impression of partiality".
The fired Federal Bureau of Investigation director said ultimately it was up to Mueller to make a determination whether the president crossed a legal line.