Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.) on Tuesday urged Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) to hold a vote on a bill to protect special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE.

“I would certainly vote for it,” Graham told reporters, according to Reuters. “I don’t see any movement to get rid of Mueller. But it probably would be good to have this legislation in place just for the future.”

Graham co-sponsored the legislation to protect the Mueller investigation in April 2018. It would codify Department of Justice regulations that say only a senior official can fire Mueller or another special counsel, and would give a special counsel the ability to challenge their firing in court.

The South Carolina Republican worked with Sens. Thom Tillis Thomas (Thom) Roland TillisThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting OVERNIGHT ENERGY: EPA head questions connection of climate change to natural disasters | Pebble Mine executives eye future expansion in recorded conversations | EPA questions science linking widely used pesticide to brain damage in children Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight MORE (R-N.C.), Chris Coons Christopher (Chris) Andrew CoonsMurkowski: Supreme Court nominee should not be taken up before election Battle lines drawn on precedent in Supreme Court fight Sunday shows - Ruth Bader Ginsburg's death dominates MORE (D-Del.) and 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 (D-N.J.) on the legislation and previously voted for it in committee.

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The special counsel is examining ties between President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE's campaign and Russia during the 2016 election.

Democrats and some Republicans have raised concerns that the ouster of Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE last week threatens the investigation.

Trump replaced Sessions with Matthew Whitaker as acting attorney general, who has criticized the probe in the past.

Democratic leaders, including Minority Leader Nancy Pelosi Nancy PelosiHoyer: House should vote on COVID-19 aid — with or without a bipartisan deal Ruth Bader Ginsburg lies in repose at Supreme Court McCarthy threatens motion to oust Pelosi if she moves forward with impeachment MORE (D-Calif.), have called for Whitaker to recuse himself from the investigation.

"Given his record of threats to undermine & weaken the Russia investigation, Matthew Whitaker should recuse himself from any involvement in Mueller’s investigation," she tweeted. "Congress must take immediate action to protect the rule of law and integrity of the investigation."

McConnell said last Friday that legislation protecting Mueller was not needed because he doesn't believe President Trump will fire the special counsel.

Sen. Chuck Grassley Charles (Chuck) Ernest GrassleyThe Hill's 12:30 Report: Ginsburg lies in repose Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy Read: Senate GOP's controversial Biden report MORE (R-Iowa), the chairman of the Judiciary Committee, told reporters Tuesday that he supported the bill to protect Mueller but would not lobby McConnell on allowing the legislation to move forward, Reuters reported.

– Jordain Carney contributed to this report, which was updated Nov. 14 at 12:15 p.m.