Legally-speaking, experts say that that job belongs to Deputy Attorney General Rod Rosenstein, though Trump could order Rosenstein to fire Mueller. Rosenstein said he has seen no evidence of good cause to fire the special prosecutor overseeing the Russian Federation investigation. So that is what I would do. Rosenstein would be the one to fire Mueller, which he repeatedly assured senators Tuesday he would not consider without "good cause".
Trump reportedly became aware of the longtime relationship between Mueller and Comey after being alerted to reports on Breitbart News and other conservative media outlets.
Firing Mr Mueller would be politically explosive and would raise new questions about Mr Trump, whose dismissal of Mr James Comey as Federal Bureau of Investigation chief led to charges of obstruction of justice - and to Mr Mueller's appointment.
White House press secretary Sean Spicer said on June 6 that he had "not discussed" whether Trump felt comfortable with Mueller as special counsel.
"I have determined that a special counsel is necessary in order for the American people to have full confidence in the outcome", Rosenstein said last month. Though some in the White House have preached caution, fearing a repeat of the firestorm over Comey's firing, many in Trump's orbit - including his son Donald Trump Jr. and adviser Newt Gingrich - have deemed Mueller biased and worthy of dismissal.
Attorney General Jeff Sessions recused himself from all matters having to do with the Trump-Russia investigation because of his own conversations with Russian officials during the Trump transition.
Facebook dabbling with 'Artificial Intelligence' to remove terrorist content
When material is identified and removed, algorithms "fan out to try to identify related material that may also support terrorism". Artificial intelligence will largely be used in conjunction with human moderators who review content on a case-by-case basis.
Now Mr. Gingrich has been joined in this chorus by a Trump confidant and golf-buddy, the President of Newsmax, who says the President is contemplating firing Mueller. "With respect to this subject, only the president or his attorneys are authorized to comment".
Mueller's investigation will oversee an FBI probe into whether members of Trump's campaign team and his associates colluded to help Russian Federation with its interference in the election.
Rosenstein was likely referring to the possibility that Mueller would investigate whether Sessions violated his recusal or whether Comey's firing might have been an effort to obstruct justice.
The report stated that Trump was angered when he learned of the relationship and made plans to dump Mueller before being convinced it would be a disastrous move. "Mr Ruddy never spoke to the president regarding this issue", an official said.
They have done it before: Think about how it floated the idea of Mueller's potential conflicts of interest and remember those charges of Democratic ties to acting FBI Director Andrew McCabe?
But people close to Mr. Trump say he is so volatile they can not be sure that he will not change his mind about Mr. Mueller if he finds out anything to lead him to believe the investigation has been compromised.
Peter Carr, a spokesman for Mueller, declined to comment on Ruddy's remarks.