Under current rules governing how a special counsel can be removed, Trump can't fire him directly. But there is increasing concern on both sides of the aisle in Congress that the president, who has repeatedly dismissed the Russia probe as "a witch hunt," could just waive those regulations and oust him.
Deputy Attorney General Rod Rosenstein, who appointed Mueller as special counsel, assured Congress that he would not fire him without cause.
But legislators are seeking to check executive power by making any indefensible firing of the special counsel far tougher to do.
One bill would provide for a judicial reviewSens. Chris Coons (D-Del.) and Thom Tillis (R-N.C.) on Thursday introduced the Special Counsel Integrity Act which calls for judicial review in the event any special counsel is fired without justification.
The bill -- which is retroactive to May 17, the day Mueller was appointed -- focuses on judicial recourse in case of an unwarranted removal of a special counsel,
The Delaware senator said the legislation would create "a private right of action for a special counsel, empowering him to seek judicial review" in the event of a firing and to get a determination within 14 days of the action being filed.
"This reflects, in my view, a broader bipartisan concern that the president might take inappropriate action to interfere with the ongoing important work of Special Counsel Bob Mueller," Coons told a small gathering of reporters Thursday.
Sen. Tillis said the bill would provide a check on the president's power to fire a special counsel.
"The president would maintain the power to remove the special counsel, but we would just want to make sure that it had merit and have that back-end judicial process," Tillis told CNN.
Another bill seeks to prevent unwarranted dismissalEarlier this week, another bipartisan pair of senators, Lindsey Graham (R-S.C.) and Cory Booker (D-N.J.) unveiled legislation with a similar goal. But their bill seeks to prevent an unwarranted dismissal by providing an expedited review of the decision by a three-judge panel in federal court.
Coons said the bill by him and Tillis would work in tandem with the one by Graham and Booker, for he called "a belt-and-suspenders" approach.
The two bipartisan legislative efforts could be merged into one bill in coming weeks but would still have a long way to go before becoming law, including facing any potential presidential veto.
Concern rose among senators of both parties after the president attacked Attorney General SessionsTrump's recent, repeated public attacks on Attorney General Jeff Sessions over his recusing himself from any involvement in the Russia investigation has sparked bipartisan concern and led to some speculation that the president could fire Sessions and appoint in his place an attorney general who could take over the Russia probe and potentially remove Mueller.
Republican Sen. Graham warned late last month that any move by Trump to remove Mueller "could be the beginning of the end of the Trump presidency, unless Mueller did something wrong."
Trumps' personal attorney said the president "isn't thinking about firing Bob Mueller, so this speculation is just incorrect."
And the new White House chief of staff, John Kelly, has assured Sessions that his job is safe.
But some lawmakers want to try to prevent any potential presidential interference with Mueller's probe.
Coons said that based on the concerns he has heard from Senate colleagues, "If the president were to fire the special counsel, the Senate might promptly take action to reappoint him."