"I am not going to support witnesses being called for by the president. I am not going to support witnesses being called for by Sen. [Charles] Schumer [D-N.Y.] ," Graham said, adding that he wants as "short a trial as possible."

Graham's comments come as Senate Republicans are expected to delay a decision on whether to let either side call witnesses as part of the Senate trial until after the proceeding starts in January.

Trump indicated this week that he would defer to McConnell on impeachment trial witnesses. White House officials had laid out a wish list of potential witnesses, including Hunter Biden , the whistleblower at the center of the House impeachment inquiry and House Intelligence Committee Chairman Adam Schiff (D-Calif.).

Graham, however, argued Wednesday that the place to dig into the conservative allegations against Biden and Ukraine was outside of the impeachment process.

"I don't know if anything wrong happened, but somebody needs to look. ... The floor of the Senate during impeachment is not the way to do this," he said.

"We can look at these accusations outside of impeachment. So I'm going to tell the president no to his witness request because I think what's best for the country is to get this behind us," he added.