Donald Trump wants late Senator Lindsey Graham's sister to fill the vacant seat left behind after the lawmaker's sudden death. 

'I recommended, to Governor Henry McMaster, Lindsey Graham’s wonderful sister, Darline, to serve as interim Senator from the Great State of South Carolina,' the President wrote on social media. 

'This would be a fabulous tribute to Lindsey, who loved her dearly!' 

Darline Graham Nordone, the late senator's younger sister, has never served in public office. 

'If she took a role on, she would be a great representative of our country,' Graham said of his sibling in 2015. 'I can't think of a better person to represent our country in an event than my sister.'

Tim Scott, South Carolina's second senator, suggested that Nordone was open to the idea. 'After speaking with Darline, there is no one better who understands Lindsey’s love for family, our state, and our country,' Scott posted on X.

Senate Republican Leader John Thune told CNN that it 'makes a lot of sense' to appoint Darline to her brother's vacated seat, indicating that he is embracing the President's suggestion. 

Within hours of Graham's death, there was jockeying among Republicans to position themselves to fill the seat. 

South Carolina Governor McMaster spoke Monday afternoon about the late senator and the vacancy in Congress left by his death. 

At the ceremony, the Governor appointed Darline to her late brother's seat. 

It is unclear whether Nordone's appointment would be a 'caretaker' selection, meaning she would not seek the office after her current term ends in January, or if she would formally announce a run for his seat in a special primary election. 

Graham's death kicks off a one-week registration period for a special primary election so that a new candidate can swiftly fill the vacancy, according to South Carolina law. 

Registration is slated to begin July 21, and the election would be held two Tuesdays later, on August 11. 

If there is a runoff for the special primary election, it would be held on August 25.

The winner of the special primary election would go on to face Democratic candidate Annie Andrews in the November race. 

Already there is speculation about which South Carolina politicians may hop into the special primary election. 

Lieutenant Governor Pamela Evette, Fox News host and former Congressman Trey Gowdy, Congresswoman Nancy Mace, Congressman Ralph Norman and more have been mentioned as possible candidates. 

'Just when I thought I was out… they pull me back in…,' Mace, who is retiring from Congress at the end of her term, wrote on social media on Sunday morning after the news of Graham's death broke. 

The post stirred belief that she will run for the open Senate seat.

It also provoked controversy in the GOP after Republicans accused Mace of callously floating a potential Senate bid just hours after Graham's death was announced. 

A spokesman for her campaign told the Daily Mail that 'Lindsey Graham was a mentor to Nancy Mace, and one of the funniest, quickest people she ever served alongside. Anyone who knew him knew he loved a good line, and told more of them than anybody in Washington.'

Speaking with CBS News on Monday, Evette declined to comment on whether she is interested in running for the Senate seat. 

'Today is celebrating what a great life the senator has given to this nation,' she said.

Meanwhile, Norman is expected to seek the vacated Senate seat, sources familiar with his thinking told FITSNews. 

A source told the outlet that Norman is 'strongly considering' a bid for the seat, though he didn't want to say anything publicly right after Graham's death. 

Lindsey and Nordone were incredibly close, and after the siblings' parents died 15 months apart in the 1970s, the Senator, then 21, legally adopted his teenage sister and helped raise her. 

The senator never married or had children but noted that he did have a family, namely his younger sister. 

The siblings were raised in Central, South Carolina, near Clemson University. Their parents operated a bar and pool hall. The young Grahams lived in a room in the back of the establishment. 

'He’s kind of like a brother, a father and a mother rolled into one,' Nordone told the New York Times in 2015. 

The senator kept close tabs on his younger sister as the two grew up without their parents. 

The Republican's law school friends told NPR that Graham would visit his sister on weekends and would inquire about whether she was keeping curfew and who she was spending time with. 

After joining the Air Force as a military lawyer, he adopted Nordone, ensuring that if anything happened to him, his benefits would flow to her.