Once one of the US president's fiercest critics, Senator Lindsey Graham has recently championed his country's leader. He has previously stated he would like to lead the committee, were the vacancy to open up.
The committee is the first to review the president's choices for federal government and judicial posts, including the judges he would like to place on the Supreme Court.
In his year in office Mr Trump has pushed through a series of conservative judges to federal benches, including two justices onto that court, including controversial choice Brett Kavanaugh.
Mr Grassley has said that he would like to take over at the Senate Finance Committee which writes tax law. Retiring senator Orrin Hatch has recently vacated that seat.
The Judiciary Committee came under the spotlight during the confirmation of Justice Kavanaugh, who was accused by at least three women of sexual misconduct.
He denied those accusations, and was later confirmed to the bench.
Should Mr Graham become the chairman of the Judiciary Committee, then Mr Trump would have a powerful ally running the powerful legislative body.
During the Kavanaugh hearings, Mr Graham repeatedly chastised Democrats for the treatment of the nominee, and praised the candidate's career as a judge in the federal judiciary.
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