Sen. Lindsey Graham Lindsey Olin GrahamGraham: GOP will confirm Trump's Supreme Court nominee before the election Fox's Napolitano: Supreme Court confirmation hearings will be 'World War III of political battles' Grassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee MORE (R-S.C.) chimed into speculation that 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 could be tapped to replace John Kelly as Homeland Security secretary, saying the title just "doesn't feel right" on Sessions.

"AG Jeff Sessions has a good ring to it," Graham wrote on Twitter. "Highly qualified, committed to the rule of law, tough on crime, and fiercely independent."

AG Jeff Sessions has a good ring to it.



Highly qualified, committed to the rule of law, tough on crime, and fiercely independent. (1/2) https://t.co/nwt2pi1iYc — Lindsey Graham (@LindseyGrahamSC) July 29, 2017

"DHS Secretary Jeff Sessions doesn't sound right, doesn't feel right," he continued. "Bad idea."

DHS Secretary Jeff Sessions doesn't sound right, doesn't feel right.



Bad idea. (2/2) https://t.co/nwt2phJHzC — Lindsey Graham (@LindseyGrahamSC) July 29, 2017

Included in his tweets was a link to the Politico report saying that Sessions is among those being discussed by department staffers as a possible replacement for Kelly, whom Trump named White House chief of staff on Friday.

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Sessions's future at the Justice Department has been the subject of speculation in recent days after Trump launched a series of public attacks at the attorney general.

Trump has complained recently about Sessions's decision to recuse himself from the law enforcement investigation into Russian election meddling, and, at one point, called him "beleaguered" in a tweet.

Sessions has said he has no plans of resigning from the Justice Department and that he is willing to serve as long as the president wants him to.

The mere thought of Trump firing Sessions has drawn ire from conservatives in Congress, including Graham, who said on Thursday that "there will be holy hell to pay" if Trump ousts his attorney general.