COLUMBIA, S.C. (AP) — Sen. Darline Graham has privately expressed interest in running for a full U.S. Senate term after getting appointed as a temporary replacement for her late brother, Lindsey Graham, according to four people familiar with the deliberations.

The people, who were not authorized to speak publicly, said she has started having conversations about a potential campaign. Two of them said Darline Graham has been talking to the White House.

Although President Donald Trump was enthusiastic about her filling the seat for a time, it’s unclear if he would support her campaign. Trump has previously suggested he could back a potential candidacy from Rep. Russell Fry.

Plans for Lindsey Graham’s funeral were also announced on Friday. There will be a service in Washington on July 28 and more in South Carolina on July 29.

Darline Graham’s eventual decision could dramatically shake up the scramble to fill her late brother’s seat after he died last weekend. The filing period for a special primary runs from July 21 to July 28, and the primary is scheduled for Aug. 11.

Several other noteworthy politicians — including Fry, Rep. Nancy Mace, Rep. Ralph Norman and Lt. Gov. Pamela Evette — have been eyeing a run.

Darline Graham’s conversations were first reported by Semafor.

South Carolina Gov. Henry McMaster appointed Darline Graham to serve the remainder of her brother’s term, which ends in January.

The first woman to represent the state in the Senate, Darline Graham called it “such an honor,” as dozens of her brother’s staffers and campaign advisers stood behind her, some with eyes glassy from welling tears.

“Lindsey has always been there for me. And now, I will be there for him,” she said.

Lindsey Graham died on Saturday at age 71. A preliminary report from the medical examiner said he suffered a tear in his aorta.

He never married or had a family of his own, but his sister was often by his side for the political touch points of his career, speaking at events and appearing in some of his campaign ads.

In his announcement on Monday, McMaster made no reference to her as a placeholder or symbolic appointment.

However, a person familiar with McMaster’s thinking but unauthorized to speak publicly said the governor, in selecting Darline Graham, had never contemplated that she would run for the seat herself.

Sen. Tim Scott, another South Carolina Republican, said he would not endorse any candidate in the primary because he also serves as chairman of the National Republican Senatorial Committee.

But, he said, “as Tim Scott, the voter of South Carolina, I might indeed wade into the water at some point.”

“I think the truth of the matter is that Darline has so far been off to a remarkable start,” Scott told reporters, asking about her as a possible special primary contender. “‘Why not her?’ would be my question.”

When he died, Lindsey Graham had millions in his campaign account and was expected to raise much more heading into the general election. But those aren’t funds that Darline Graham could directly access, if she were to run, according to Bradley A. Smith, a former chairman of the Federal Election Commission.

Under federal rules, Lindsey Graham’s campaign would be limited to transferring just $2,000 to a potential Darline Graham candidacy. However, Smith said there is no limit on how much it could transfer to the National Republican Senatorial Committee, which could — thanks to a Supreme Court decision last month — “spend an unlimited amount in coordination with Darline’s campaign.”

“It can’t be earmarked for Darline’s campaign, but in those circumstances I’m sure that the party will make sure she’s not short of cash,” said Smith, now serving as a professor at Capital University Law School in Ohio.

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Kim reported from Washington. Associated Press reporter Thomas Beaumont contributed from Des Moines, Iowa.

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Meg Kinnard can be reached at http://x.com/MegKinnardAP