South Carolina Republican Sen. Darline Graham, sworn in earlier this week to serve the remainder of her late brother's term, reportedly told the White House she may be interested in running for the seat.

The unexpected development could further reshape an already crowded Republican primary to succeed the late Sen. Lindsey Graham, one of President Donald Trump's closest allies.

According to Semafor, Graham informed White House officials Thursday that she is considering entering the race for the full Senate term, just days after Republican Gov. Henry McMaster appointed her to fill her brother's seat through the end of the year.

Trump had urged McMaster to appoint Graham as an interim senator, calling the move "a fabulous tribute" to her brother.

The appointment was widely viewed as giving the White House more time to decide whom Trump would endorse in the Aug. 11 Republican primary.

If Graham runs, however, that calculus could change.

The freshman senator was sworn in Tuesday and quickly got to work, joining Sen. Richard Blumenthal, D-Conn., in introducing legislation to strengthen sanctions on Russia.

It remains unclear whether Trump would back her candidacy or endorse another Republican in what is shaping up to be one of the GOP's most closely watched races this year.

Businessman Mark Lynch, who unsuccessfully challenged Lindsey Graham in last month's primary, has already announced plans to run.

Others considering bids include Reps. Nancy Mace, Russell Fry, and Ralph Norman, Lt. Gov. Pamela Evette, and former Rep. Mark Sanford.

National Republican Senatorial Committee Chairman Tim Scott, R-S.C., praised Graham's early performance this week, saying she has been "off to a remarkable start" and could be "a seriously good fit for the state."

Sen. Ted Cruz, R-Texas, told Semafor he is waiting to see what Trump decides.

"Like many Republicans, I am waiting to see what the president decides, and watching with great interest," Cruz said.

Graham became South Carolina's first female U.S. senator after taking the oath Tuesday.

She has never held elected office, but previously worked as an optician and served in several South Carolina state agencies.

Lindsey Graham, who raised his younger sister after their parents died, died unexpectedly last weekend at age 71 from an aortic dissection, according to a preliminary report from the Washington medical examiner.

Under South Carolina law, the Republican nominee will be chosen in an Aug. 11 special primary, with an Aug. 25 runoff if no candidate wins a majority.

The GOP nominee will face Democrat Annie Andrews in the Nov. 3 general election.

The Associated Press contributed to this report.