"With respect to this subject, only the president or his attorneys are authorized to comment".
A spokesman for Trump's attorney Marc Kasowitz fiercely denied the allegations.
And deputy White House press secretary Sarah Huckabee Sanders said simply: "Chris speaks for himself".
Mr Trump is yet to comment publicly on the matter and White House spokesman Sean Spicer has told Washington media Mr Mueller's sacking is unlikely.
After Comey's testimony, Trump said he had been vindicated because his former FBI director confirmed telling Trump on three occasions that he was not under investigation. He said those concerns included the interview for the Federal Bureau of Investigation post and connections between Mueller's law firm and other White House officials.
"There's some real conflicts", Ruddy said. Any such step would face a steep hurdle as it would require approval by the U.S. House of Representatives, which is controlled by Trump's fellow Republicans. "I know for a fact that he was under consideration and that the president did talk with him in the days before he was named special counsel. And I think it would be odd that he would have a confidential conversation and then a few days later become the prosecutor of the person he may be investigating".
Accusations of obstruction arose last month when Trump fired FBI Director James Comey.
Under current Justice Department regulations, firing Mr Mueller would have to be done by attorney general Jeff Sessions' deputy Mr Rosenstein, not the president, though those regulations could theoretically be set aside. "I mean, these are people who are going to be after [President Donald] Trump", Gingrich told ABC News Chief Anchor George Stephanopoulos on "Good Morning America" today, adding that he believes the investigation should be curtailed given the biases associated with the case.
Ruddy first made the bombshell assertion that Trump was considering dismissing Mueller to PBS' Jody Woodruff on "PBS Newshour" Monday night. "Look who is hiring".
Earlier this week, former House Speaker Newt Gingrich reportedly told radio host John Catsimatidis that Congress should "abolish the independent counsel".
But a source close to the President said Trump is being counseled to steer clear of such a dramatic move like firing the special counsel.
Reports that Trump was considering firing Mueller surfaced last week, again citing unnamed sources.
She, further, insisted that Sessions should fire Mueller, now that the President is not under investigation. "Don't waste time trying to undermine one of your few allies".
Former Alberta UFC fighter dead after knockout hit
RealFightStories.com reported Saturday night that Hague was on life support as his family made arrangements for organ donations. Writing on Facebook the following day, his sister Jackie Neil said: "Thanks folks for all your messages and kind words".