Mueller has been silent since he was named to head the Russian Federation investigation on May 17, a week after Trump fired FBI chief James Comey expressing frustration over the probe.
Spicer had said that Ruddy was at the White House Monday to meet with White House aides, but did not speak with the president.
Since then, lawmakers have raised questions about a possible third meeting at a Washington hotel, though the Justice Department has said that did not happen. Legally-speaking, experts say that that job belongs to Deputy Attorney General Rod Rosenstein, though Trump could order Rosenstein to fire Mueller.
Honestly, I really hope he does try to fire him.
Both Rosenstein and Sessions are testifying Tuesday on Capitol Hill.
Spokeswoman Sarah Huckabee Sanders told reporters aboard Air Force One that "while the president has the right to" fire Robert Mueller, "he has no intention to do so".
But Ruddy opened a new line of questions about Mueller's impartiality - the fact that Trump had considered Mueller for the Federal Bureau of Investigation director's job before he was named special counsel.
High-profile supporters of President Donald Trump are turning on special counsel Robert Mueller, the man charged with investigating Russian interference in the USA election and possible collusion with Trump's campaign.
In Mueller's case, Trump would have to ask Rosenstein to do the firing.
Here's why. According to the rules, technically only the attorney general can fire a special counsel. That, to me, is the smartest thing to do, the best thing to do, and that's what I think hopefully will happen.
Angered by reports in Breitbart News and other conservative news outlets that Mr. Mueller was close to Mr. Comey, Mr. Trump in recent days has repeatedly brought up the political and legal implications of firing someone he now views as incapable of an impartial investigation.
What is clear is that he could order the Justice Department to ax Mueller, which may result in Rosenstein's departure and would certainly intensify the uproar over the investigation.
Sessions in March stepped aside from the federal investigation into contacts between Russian Federation and the presidential campaign after acknowledging that he had met twice past year with Kislyak.
"I won't mince words: You're not the witness we were supposed to hear from today", said Sen. Brian Schatz, D-Hawaii. He is at the Senate committee and goes to the House one at 2 p.m. ET.
Ruddy had been at the White House the same day, though White House press secretary Sean Spicer said he did not meet with the president. If Mr Rosenstein refused, Mr Trump could fire him, too. Mr Ruddy said Mr Mueller has some "conflicts" because his former law firm, Wilmer Hale, also representing Ms Ivanka Trump, the President's daughter, and her husband, Mr Jared Kushner. "Mr Ruddy never spoke to the president regarding this issue", an official said. The questions came after a Trump associate suggested on Monday that. "And there is no collusion between certainly myself and my campaign, but I can always speak for myself - and the Russians, zero", Trump responded.
Criticism of special counsel Robert Mueller used to be off limits.
Still, top Democrats on the Senate Appropriations subcommittee fumed that Sessions had abruptly canceled his appearance there, with Sen. However, after facing numerous complaints, Bork ended up appointing another special prosecutor who, after nine months of investigation, found enough damning information that Nixon made a decision to resign.
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