Rep. Mick Mulvaney (R-S.C.) said he won't run for the Senate against any of his colleagues in South Carolina's congressional delegation — including Sen. Lindsey GrahamLindsey Olin GrahamTop Louisiana health official rips Cassidy over ObamaCare repeal bill Senate Dems hold floor talk-a-thon against latest ObamaCare repeal bill Overnight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions MORE (R-S.C.). But he told The Hill on Wednesday that he wouldn't rule out a bid for the seat being vacated by Sen. Jim DeMint (R-S.C.) if someone else is picked to fill out DeMint's term.

Mulvaney was left off South Carolina Gov. Nikki Haley's (R) shortlist for possible replacements for DeMint, despite Mulvaney saying last week he thought he'd be considered. Mulvaney and Haley have, at times, had an adversarial relationship, sources said.

Mulvaney offered full-throated endorsements for Reps. Tim ScottTimothy (Tim) Eugene ScottWhy President Trump’s 'both sides' argument has merit GOP senator: 'There is no realistic comparison' between antifa and white supremacists Trump on white supremacists: ‘Pretty bad dudes on the other side also' MORE (R-S.C.) and Trey GowdyTrey GowdyGowdy: Sarah Sanders doesn't get say whether Comey broke the law Trump condemns Rice's unmasking: 'What she did was wrong' Sessions, Coats push for permanent renewal of controversial surveillance law MORE (R-S.C.), calling his two House colleagues who are on the list "friends." He sounded less than enthusiastic about a third name, former South Carolina first lady Jenny Sanford (R). Whoever is chosen will face an election in 2014.

"I think all the candidates on her list are good. Obviously I have a special affinity for Mr. Gowdy and Mr. Scott. Both of them would make excellent senators," he said. "I don't know the other people as well. I was surprised to see Jenny Sanford's name on the list — I'm not really sure why she's on the list."

Mulvaney said he knew the other two people on Haley's shortlist, former South Carolina Attorney General Henry McMaster (R) and attorney Catherine Templeton (R), "a little bit." He said he didn't know them well, but was "absolutely not" saying he opposed either being picked.

When asked if there was any chance he'd challenge Haley's pick in a GOP primary if Scott or Gowdy weren't selected, he said it depended on how they voted in the Senate.

"I don't know. I don't know enough about them," he said.

Graham is also up for reelection in 2014, and some national conservative groups hope they can entice someone to run against him in the GOP primary. South Carolina state Sen. Tom Davis (R) had been viewed as the most likely candidate, but told The Hill last week that he "probably won't" run, and hoped Mulvaney would take up the challenge.

Mulvaney knocked down that idea on Wednesday.

"I have no interest in running against Senator Graham," he said.

He also said he didn't "get the sense" that Graham would face a serious primary, despite his occasional breaks from conservative orthodoxy.

"Lindsey is a lot more conservative than probably people in the national press give him credit for ... Lindsey's reputation back home is strong. He's very well liked."

Graham told The Hill on Tuesday that he still expects a primary challenge, but predicted he'd hold on to his seat.

"I'm confident that, if I keep doing a good job, I'll be OK. But I expect someone will challenge me," he said. "I don't know what awaits me in the 2014 primary cycle, but I know what I need to be doing. I need to be a conservative voice up here that can also solve problems and I need to take care of my backyard. ... I think the reason I'm doing OK at home is that people feel like I'm trying my best and that they feel like I'll put the state's interests ahead of my own."

A recent poll showed Graham had improved his standing with South Carolina GOP primary voters and held a solid lead against any of the names that have been floated as possible challengers.