"Durham is going to look at all things criminal. He's on the case. The collusion narrative has died with the Mueller report. The corruption narrative is growing by every day," Graham said.
Durham, a Connecticut federal prosecutor, was assigned by Attorney General William Barr in April to look into the origins of the Russia investigation.
Graham said separately that Justice Department inspector general Michael Horowitz will likely soon release the findings of his investigation of the FISA warrant application process.
"Horowitz will be coming out soon, I hope, with his internal review of the FISA warrant application, and whether or not the court was defrauded by the Department of Justice and the FBI.
"Every American should be concerned about whether or not the FISA court, which is a secret court, was lied to about the source of information to use to gather a warrant. Every American should be worried about whether or not our government tried to get some foreign government to do some things we're prohibited to do by law."
Graham added it will be entertaining to watch President Trump and former Vice President Joe Biden spar as the 2020 election season heats up.
"It's going to be fun," the South Carolina lawmaker said, responding to a clip of Trump riffing on the former Delaware senator.