Story highlights Bernstein said White House aides have told him Trump has repeatedly expressed a desire to fire Mueller

He and his partner of Watergate reporting fame, Bob Woodward, drew parallels between Trump and Nixon

Washington (CNN) Veteran journalist Carl Bernstein said Sunday that President Donald Trump's lawyers are telling him what he wants to hear about the probe ending soon to prevent Trump from firing Mueller.

"There are many times he has expressed, I'm told by people in the White House, the desire to fire Mueller, the desire to pardon people under investigation including his family," Bernstein, a CNN contributor, told CNN's Dana Bash on "State of the Union." "His lawyers are telling him what he wants to hear -- that's what I'm told -- by lawyers in the White House, they're telling him what he wants to hear to keep him from acting precipitously and to go off and fire Mueller in a rage, or fire (Deputy Attorney General) Rod Rosenstein in a rage. They have an out-of-control client."

Bernstein added: "The President of the United States, in their view, is out of control most of the time, in their view, when it comes to this investigation."

Bernstein's partner of Watergate reporting fame, The Washington Posts' Bob Woodward, appeared alongside him on the program, telling Bash he expects Mueller to leave no stone unturned in the investigation.

"Mueller is going to do this job," Woodward said. "I think some of the Trump lawyers are fantasizing when they think it's going to be over quickly. There is no reason the Mueller operation is going to close up; they're going to want to be thorough."

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