Senators will be called upon to determine whether the president should be removed from office if the House of Representatives votes to pass articles of impeachment against Mr Trump this week.
However, Mr Graham, the chairman of the Senate Judiciary Committee, has said he plans to shut down an impeachment trial as quickly as possible and does not want to hear from any more witnesses on the president’s alleged misconduct with Ukraine.
“I have clearly made up my mind. I'm not trying to hide the fact that I have disdain for the accusations and the process,” Mr Graham told CNN on Sunday.
“I am ready to vote on the underlying articles. I don't really need to hear a lot of witnesses.”
The senator’s admission comes as Democrats have warned Republicans will not judge the evidence against Mr Trump impartially.
In an interview with CNN International’s Becky Anderson, Mr Graham was asked if it was appropriate for him to be voicing his disdain for the process before a trial has even begun.
“I'm not trying to pretend to be a fair juror here,” he replied.
Senate rules require lawmakers to swear an oath to do “impartial justice according to the Constitution and laws” at the beginning of an impeachment trial.
“This thing [impeachment] will come to the Senate, and it will die quickly, and I will do everything I can to make it die quickly,” Mr Graham added.
Chuck Schumer, the Democratic minority leader in the Senate, has said it is “paramount” that a fair and honest impeachment trial takes place.
Mitch McConnell, the Senate majority leader, reportedly wants a quick trial to avoid a political circus that could undermine Mr Trump’s re-election chances.
The senior Republican has already said there is “zero chance” of Mr Trump being removed from office and pledged “total coordination” with the White House during the trial.
The president is accused of withholding congressionally-approved US military aid and a White House visit to Ukraine to force its leader into announcing an investigation into Mr Biden, his 2020 election rival.
Mr Trump has denied any wrongdoing, despite a series of politically damaging testimonies from high-profile US diplomats and foreign service officials about his conduct.
A two-thirds majority is required in the Republican-controlled Senate to convict Mr Trump and remove him from office.
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