And there's a reason for their confidence: Mueller has long been widely respected by many in Washington.
Back in 2013, the Department of Justice held a farewell ceremony for Mueller, who was retiring after 12 years as FBI director.
The event featured a handful of speakers, including then-Attorney General Eric Holder, then-Deputy Attorney General James Cole and Mueller himself. Here are some of the most memorable lines:
"It appears, as he departs justice for the last time, hopefully, he will have held every position in the department save one: Attorney general. But then again, one has to wonder whether this time he's really leaving for good. When we bade him farewell in this same hall in January of 1993, we thought we were rid of him for good. Ah well, there's no sense in worrying today what might happen tomorrow."
2. Later, Margolis brought up now-former FBI Director James Comey when complimenting Mueller.
"In perilous times when this department finds it necessary to go to the mattresses, there is no one I'd rather have at my side than Bob Mueller, except of course Jim Comey," he said, which prompted laughter from the room
3. George Tenet, former CIA director under Presidents Bill Clinton and George W. Bush, touched on Mueller's "devotion to duty." He noted how Mueller was awarded a Bronze Star and Purple Heart for his service.
"He is and always will be a United States Marine, service to this country has been his life," Tenet said. "Bob Mueller has never changed. His life has been defined by trust, discipline and honor."
4. Tenet also said he and Mueller "love testifying together," which garnered laughs from the room.
"The first time I testified with him, you know, he sat there like a choir boy and never moved. I said, you know, Bob you have to learn how to emote a little bit. He said, 'I can't emote I've been trained as a prosecutor, we're not allowed to show emotion.' ... Bob and I would be in the middle of a testimony and I would say something to Mueller like, 'Bob isn't that the dumbest question you've ever heard in your life?' (And he would say,) 'shut up.'"
5. John Pistole, former deputy director of the FBI, described Mueller's positive traits:
"A leader, a man of character and integrity, a distinguished and dedicated public servant, humble, principled pragmatist, an innovator and a motivator. ... Bob has never been one to seek out the limelight, he's always been quick to give others credit."
6. Cole said one thing was very clear: Mueller "touched so many people in so much of the same way throughout their careers."
7. Holder credited Mueller with "transforming the FBI into the dynamic threat-focused organization that is today."
"Bob's work literally helped to save lives," Holder said. "And also made better the lives of people who were too often unseen or who were forgotten. He was eager to make a difference and he did."
8. Mueller himself was -- as many described him -- humble, even when taking the podium to speak at the ceremony. He received a standing ovation. But the first thing he said in his departure speech was: "Thank you, we gotta get outta here!"
9. He highlighted his love for the Department of Justice and everyone who he worked with there.
"I've always been proud to say I work for the Department of Justice because of that for which it stands -- which is an unyielding commitment to the rule of law and to the safety and security of the citizens we serve. But I've also been honored to work with the individuals who have given the Justice Department its legacy and its lasting impact. ... throughout my time here I've seen unparalleled commitment and professionalism. And I've seen firsthand the sacrifices made by those in law enforcement."
10. He ended the speech by saying he is "forever grateful" for the opportunities he was given during his career.
"While it is difficult to leave this family, I leave knowing that the work will continue under the leadership of individuals in a Department of Justice and in the FBI alike who embody the FBI's motto of fidelity, bravery and integrity in the truest and best sense of those words."
See the full video of the ceremony here