Hours after GOP Sen. Lindsey Graham’s death, President Donald Trump on Sunday said he had a preferred replacement in mind but declined to share a name out of respect for Graham.

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“I have somebody that I think would be great, but I don’t want to say it now because it’s just, you know, it’s too soon with Lindsey,” the president told NBC News’ “Meet the Press.” “I don’t want to even talk about anybody, but I do have somebody that I think is really good.”

Trump’s remarks came as Republicans are starting to scramble to find a temporary and permanent replacement for Graham, who in June won the GOP Senate primary in South Carolina and was expected to cruise to re-election to a fifth term in November.

Per South Carolina state law, GOP Gov. Henry McMaster must appoint someone to take over Graham’s post until early January.

The law also dictates the process for an election to permanently replace Graham. A special Republican primary election will be held on Aug. 11 and candidates who wish to run for Senate can file to run for the seat beginning on July 21.

Sen. Tim Scott, R-S.C., who served alongside Graham, said Sunday that he did not have any insight into who McMaster may appoint to fill the seat.

“I do know that there are at least one or two Congress members that I would expect Henry McMaster, our governor, to consider,” Scott told “Meet the Press” moderator Kristen Welker, adding later that it’s “hard to swallow that life moves so quickly, and the party doesn’t stop, ever.”

Scott said regardless of who McMaster selects as a temporary appointment, “I would imagine an open primary process would be in the best interest of South Carolinians.”

Rep. Nancy Mace, R-S.C., is strongly considering running for the now-vacant seat, according to a source familiar with her thinking. Mace ran unsuccessfully for governor in the state’s June primary.

Rep. Joe Wilson, R-S.C., publicly said that he won’t run for the seat in a post on X today, citing a conversation he had with the president and Republicans’ slim majority in the House.

“I was grateful to speak with President Trump today reminiscing about our mutual friend, Senator Lindsey Graham. I assured him my goal is to remain in the House to keep his two-vote majority for the American people!!!” Wilson wrote on social media.

Mark Lynch, a South Carolina businessman who challenged Graham in the Republican primary for Senate earlier this year, in a statement did not say whether he planned to run for the seat again.

“While we had our political disagreements, today is not a day for politics,” Lynch said. “It is a day to recognize his decades of service and to pray for everyone who knew and loved him.”