(CNN) Sen. Lindsey Graham, a key Republican on the Senate Judiciary Committee, said Thursday that President Donald Trump could replace Attorney General Jeff Sessions after the midterm elections in November.

Graham's comments make him one of the first Republicans on the Senate committee to signal an openness to Trump ousting Sessions in his first term.

In an interview with reporters Wednesday, the senator from South Carolina said ultimately it was up to Trump to decide who he wanted for the job and that while he personally likes Sessions, he said Trump deserved an attorney general he had "faith in."

"The President's entitled to having an attorney general he has faith in, somebody that is qualified for the job and I think there will come a time sooner rather than later where it will be time to have a new face and a fresh voice at the Department of Justice. Clearly, Attorney General Sessions doesn't have the confidence of the President," Graham said.

Graham added specifically, "That's an important office in the country and after the election, I think there will be some serious discussions about a new Attorney General."

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