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 said he would "totally" look into the FBI's handling of its investigations into Russian interference in the 2016 presidential election and former Secretary of State Hillary Clinton Hillary Diane Rodham ClintonDemocratic groups using Bloomberg money to launch M in Spanish language ads in Florida The Hill's Campaign Report: Presidential polls tighten weeks out from Election Day More than 50 Latino faith leaders endorse Biden MORE's emails if he becomes chairman of the Senate Judiciary Committee.

"The oversight function will be very much front and center," Graham said in an appearance on CNN.

Graham is in position to rise to chairman of the Judiciary Committee if 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 current chairman, opts to head up the Senate Finance Committee instead.

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The South Carolina Republican, who has emerged as one of 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 strongest advocates, has previously expressed a desire to look into the FBI's investigations. He has suggested on multiple occasions that a second special counsel should be appointed to probe GOP allegations of bias within the bureau.

Graham also indicated on Tuesday that he would support 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 in his investigation into Russian election interference, but cautioned that he doesn't believe there's a need for it.

“I don’t see any movement to get rid of Mueller," he said. "But it probably would be good to have this legislation in place just for the future.”

Graham co-sponsored a bill to protect the Mueller investigation in April that would codify Justice Department regulations that say only a senior official can fire Mueller or another special counsel.

Democrats and some Republicans have revived calls for legislation to protect the special counsel after Trump fired 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 as attorney general and replaced him with acting Attorney General Matthew Whitaker, who penned opinion pieces as a private citizen arguing for stifling Mueller's funding and curbing the scope of his investigation.