South Carolina's Republican governor said Friday she was working quickly to appoint a replacement to retiring Sen. Jim DeMint's seat in the U.S. Senate, writing she was looking to put a similar-minded conservative in the Upper Chamber.

"Appointing a new member of the U.S. Senate is a solemn duty, and I take this responsibility with utmost seriousness. I will make this decision in a manner that is thoughtful and dignified, but also quickly," Gov. Nikki Haley wrote Friday.

One person she wasn't looking to appoint, Haley reiterated, was herself.

"I want to make two things clear from the outset. Number one, I will not take the appointment myself. Number two, I will appoint a person who has the same philosophy of government that Jim DeMint and I share," she said. "With all the challenges we face as a state and nation, it is essential that the next senator from South Carolina be dedicated to the principles that our state most values."

DeMint announced Thursday he was retiring from the Senate after seven years to serve as president of the Heritage Foundation, a conservative think tank.

All eyes are now on Haley as the South Carolina governor decides whom to name to fill DeMint's seat. The senator has made it known in Columbia that he wants Rep. Tim Scott to be appointed to his seat, sources told CNN. If named, he would be the Senate's only African-American member.

Sources in South Carolina told CNN Thursday that DeMint has told a handful of confidantes that he would like to see Scott appointed to the seat but official DeMint staff members in Washington are pushing back at the suggestion he's trying to influence her decision.

In a statement Thursday, Haley applauded DeMint's service in the upper chamber, saying he has served "the national conservative movement exceptionally well."

Thanking DeMint for his service, Scott said in a statement "Governor Haley will now appoint a new Senator, and I know she will make the right choice both for South Carolina and the nation."

Rep. Mick Mulvaney is another name being floated as a potential replacement for DeMint. The congressman also said he has "faith Gov. Haley will appoint someone with the character, leadership, and conservatism Senator DeMint has provided South Carolinians for the past eight years."