"This process in the House is being conducted behind closed doors," he said, calling the inquiry, "illegitimate on its face."
"What the House of Representatives is doing is a process of political revenge. It is alien to American due process. It should be dismissed quickly in the United States Senate."
Graham said Congress has set precedent for how impeachment proceedings should be handled, pointing to inquiries against ex-Presidents Andrew Johnson in the 1860s, Richard Nixon in the 1970s and Bill Clinton in the 1990s. Nixon resigned before an impeachment vote could be held.
The lawmaker added he views the House's proceeding against President Trump as "unamerican at its core."
"Republicans are being shut out and if you had an inquiry vote, that allows Republicans and the president to call witnesses and to confront people accusing the president of misdeeds," he said.
He added that the office of the president will be altered because of how House Democrats are conducting their current probe.
"For the future of the presidency, we cannot allow future presidents and this president to be impeached based on an inquiry in the House that has never been voted upon, that does not allow the president to confront the witnesses against him, call witnesses on his behalf and cross-examine people that are accusing him of misdeeds."
Graham reiterated that Trump should be afforded the same abilities and rights that Nixon and Clinton enjoyed.
"And, I'm insisting that Donald Trump be given the same rights every American has if you're given a parking ticket -- to confront the witnesses against you," he said.