Treasury Secretary Scott Bessent, a pugnacious ally of President Donald Trump, has been “fielding calls from people asking him to run” for the U.S. Senate seat left by the late Sen. Lindsey Graham (R-S.C.), Politico reported on Sunday.The Associated Press reported the same development.Graham, 71, died from a torn aorta due to cardiovascular disease, his office said over the weekend.His absence leaves the GOP with a thin majority in the upper chamber before the midterms. Graham was running for his fifth term after winning the Republican nomination.Bessent is a South Carolina native who has maintained a home there while in Washington, Politico noted.He was listening to operatives’ pleas for him to enter his hat in the ring, a person “familiar with the communications” told Politico. But another source close to Bessent said he wants to stay put.Citing another anonymous source who has had private conversations with Bessent, The Associated Press wrote that Bessent “enjoys working for the president.”Scott Bessent is taking phone calls from power brokers hoping he'll run for Lindsey Graham's seat.NurPhoto via Getty ImagesThe president told NBC News that he had “someone in mind” for the race but didn’t name the person.Meanwhile, Gov. Henry McMaster (R) is tasked with selecting a temporary replacement to serve out Graham’s fourth term through January, while a special primary is set up for Aug. 11 to elect a new GOP nominee to face Democrat Annie Andrews in the November election.Rep. Nancy Mace teased a run to fill Graham’s seat despite the lame-duck congresswoman finishing fifth in the gubernatorial primary ― and that earned her lots of ridicule.