Rep. John FlemingJohn Calvin FlemingThe Hill's 12:30 Report: Dems aim to end anti-Semitism controversy with vote today Former congressmen, RNC members appointed to Trump administration roles Overnight Energy: Watchdog opens investigation into Interior chief | Judge halts Pruitt truck pollution rule decision | Winners, losers in EPA, Interior spending bill amendments MORE (R-La.) says he's “very interested” in running for Sen. David VitterDavid Bruce VitterGrocery group hires new top lobbyist Lobbying World Senate confirms Trump judge who faced scrutiny over abortion views MORE’s (R-La.) seat should Vitter be elected governor.

“I’m very interested in that possibility,” Fleming said in an interview with Roll Call.

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“Sen. Vitter is quite conservative, and I think we need to replace a good strong conservative with another conservative,” he added.

Vitter has said he intends to run for governor next year to replace Gov. Bobby Jindal (R). If he steps down from the Senate, an interim senator would fill the seat and an election would be held for the position in 2016.

Fleming considered challenging Sen. Mary LandrieuMary Loretta LandrieuCongress needs to work to combat the poverty, abuse and neglect issues that children face Dems wrestle over how to vote on ‘Green New Deal’ Lobbying world MORE (D-La.) this year but deferred to Rep. Bill CassidyWilliam (Bill) Morgan CassidyA cash advance to consider Bottom Line I'm not a Nazi, I'm just a dude: What it's like to be the other Steve King MORE (R-La.), who unseated the Democratic incumbent. Landrieu’s loss underscores the favorable position for Republicans in the state, something Fleming said would be an advantage for him if he runs.

“It’s very clear that Louisiana is gonna be voting for Republicans for statewide elections going forward, because that’s just where we are as a state. We’re a conservative state, we’re a red state, and we need to continue bringing our Louisiana values up here,” he said. “And I think that would be a great opportunity for me to do it.”

The conservative Fleming was elected to Congress in 2008.