Sen. Chuck Grassley Charles (Chuck) Ernest GrassleySenate Republicans face tough decision on replacing Ginsburg What Senate Republicans have said about election-year Supreme Court vacancies Biden says Ginsburg successor should be picked by candidate who wins on Nov. 3 MORE (R-Iowa) signaled on Monday that his committee could take up two bills aimed at protecting Robert Mueller, the special counsel for the investigation into potential ties between President Trump's campaign and Russia.

"We're looking into it, and there's a good chance we'll have a hearing," Grassley, chairman of the Judiciary Committee, told reporters.

He added that no decision has been made on scheduling a hearing.

Lawmakers have introduced two bills that would put checks on the Trump administration's ability to fire Mueller.

One, from GOP Sen. Lindsey Graham (S.C.) and Democratic Sen. Cory Booker Cory Anthony BookerBipartisan praise pours in after Ginsburg's death DHS opens probe into allegations at Georgia ICE facility Democratic lawmakers call for an investigation into allegations of medical neglect at Georgia ICE facility MORE (N.J.), would require a judge to approve a Justice Department request to fire Mueller or any other special counsel.

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Another, from GOP Sen. Thom Tillis Thomas (Thom) Roland TillisTrump supporters chant 'Fill that seat' at North Carolina rally Momentum growing among Republicans for Supreme Court vote before Election Day Vulnerable GOP incumbents embrace filling Supreme Court seat this year MORE (N.C.) and Democratic Sen. Christopher Coons Christopher (Chris) Andrew CoonsBiden promises Democratic senators help in battleground states Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (Del.), would let Mueller or any special counsel challenge their firing in court.

Tillis told CNN last week that the Judiciary Committee would hold a hearing in the next two weeks.

The Judiciary Committee is currently running an investigation into interference in the 2016 election, potential attempts by the Obama or Trump Departments of Justice to interfere in FBI investigations and the firing of former FBI Director James Comey.

Trump and his allies have lashed out at Mueller, who is probing Russia's interference in the 2016 election and any ties to the Trump campaign. The war of words has raised concern that Trump or the Justice Department could try to fire Mueller.