Special counsel Robert S. Mueller III.President Trump has "no intention" of firing the special counsel investigating Russia's interference in the 2016 presidential election, a senior spokeswoman for Trump told reporters traveling with the president Tuesday.&ldquo;While the president has the right to, he has no intention to do so,&rdquo; Deputy White House Press Secretary Sarah Huckabee Sanders said when asked whether Trump was&nbsp;considering firing special counsel Robert S. Mueller III.Sanders also said that Trump saw part of Atty. Gen. Jeff Sessions'&nbsp;testimony before the Senate Intelligence Committee. Trump&nbsp;&ldquo;thought that Atty. Gen. Sessions did a very good job and, in particular, was very strong on the point that there was no collusion between Russia and the Trump campaign,&rdquo; she said.Whether Trump does, in fact, have the authority to fire the special counsel is an unsettled legal issue, but Trump appears to have been at least thinking about the idea.Deputy Atty. Gen. Rod Rosenstein, who appointed Mueller, testified Tuesday on Capitol Hill that under Justice Department regulations, he is the only official empowered to fire a special counsel.Asked what he would do if Trump ordered him to fire Mueller, Rosenstein said, &ldquo;I&rsquo;m not going to follow any order unless I believe they are lawful and appropriate orders.... It wouldn&rsquo;t matter to me what anybody said.&rdquo;Christopher Ruddy, a conservative publisher and a&nbsp;longtime friend of Trump, said Monday that Trump was considering removing Mueller,&nbsp;a former FBI director who has been praised for his credibility by Republican and Democratic lawmakers.Sanders declined to describe Trump's current opinion of Mueller, who was named special counsel last month by Rosenstein. Since his appointment, Mueller&nbsp;has hired a seasoned group of investigators and former prosecutors to look into potential links between Trump's campaign and Russian government officials.Mueller was interviewed by Trump to be FBI director on the day before Rosenstein&nbsp;tapped Mueller to run the Russia investigation, Sanders said.&ldquo;I do know that he did interview him, I believe, the day before he was named as special counsel, and beyond that and what I said earlier, I don&rsquo;t have anything to add,&rdquo; Sanders said.Mueller had been FBI director from 2001 to 2013. It is unclear whether Mueller was interested in returning to that&nbsp;job.Last week, Trump picked Christopher A.&nbsp;Wray to head the bureau and replace former&nbsp;Director James B. Comey,&nbsp;who Trump fired on May 9. Wray is&nbsp;a former federal prosecutor&nbsp;who recently defended Gov. Chris Christie of New Jersey in the so-called Bridgegate scandal.