The meeting took place in Trump Tower in NY and records indicate the President was in the building at the time.
He has the authority to prosecute any crimes uncovered during his investigation, and he was given wide authority to investigate whether Trump or his associates colluded with the Kremlin to win the White House.
"I have no indication the president is going to fire Mueller", he said, "his lawyer said today, here recently, that they wanna get this over with as quickly as possible".
The programme's host George Stephanopolous asked Ms Conway why Mr Trump's surrogates have differing views of the President's involvement and knowledge of that meeting.
Stephanopoulos let Conway know that was not what he was asking, but she continued along the same line of saying that this is something that has not been discussed by Trump. If you like your plan, you can keep your plan. How do you explain that, can the president and his team get control of that, and be open and truthful about the Russian Federation investigation?
Ms Conway ended the interview by calling the FBI investigation into alleged ties and collusion between the Trump campaign team and Russian Federation "fabricated" but offered no evidence for her reasoning. "You are changing the subject going back to President Obama and Hillary Clinton".
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Butowsky said that Wheeler complained to him that he was misquoted, but that he has emails showing him approving the quotes. Butowsky told the outlet that he did not share a draft with Trump and he was "joking" about the president's involvement.
Buried deep in a Freedom of Information Act document release last week to a conservative group were a series of emails that pertained to how the Justice Department handled questions from reporters about a 2016 airport tarmac meeting between former President Bill Clinton and then-Attorney General Loretta Lynch - the emails included a recipient named, "Elizabeth Carlisle", which reports now indicate was the email alias for Lynch.
"Let's talk about telling the truth", Conway snapped. "If you like your doctor, you can keep your doctor".
"I can only imagine how the country would react if Robert Mueller were fired just because the president [didn't] like the investigation", he continued.
"Benghazi happened because of a video", Conway said. "It needs to go up".
However, Democratic Rep. Adam Schiff said in a separate interview on the program that while the move was "not unexpected", it was significant because it showed the investigation had reason to move forward.
Special Counsel Robert Mueller departs after a closed-door meeting with members of the Senate Judiciary Committee about Russian meddling in the election. "What is this investigation really about?"