Whitaker, previously the chief of staff for the attorney general, has expressed skepticism over the special counsel's investigation into Russian meddling in the 2016 election, leading some Democrats to fear that he would not be neutral in overseeing the probe.
Republican Senator Jeff Flake and Democrat Chris Coons had said they would push the measure after Trump fired Attorney General Jeff Sessions and tossed out more than a century of precedent to name Sessions chief of staff Matt Whitaker as acting attorney general on November 7.
Mueller's probe has already resulted in guilty pleas from several former Trump insiders, including ex-national security adviser Mike Flynn, former campaign chairman Paul Manafort and longtime lawyer and fixer Michael Cohen, among others. "They have found no collusion and have gone absolutely nuts", the president tweeted, regarding special counsel Robert Mueller's investigation into Russian collusion during the 2016 election. They won't even look at all of the bad acts and crimes on the other side.
Thursday morning, the president fired off a quartet of tweets slamming the Mueller investigation.
He predicted universities will someday study what Mueller and his "gang of Democrat thugs" have done to destroy people.
"It's been nearly a week since we called on Matthew Whitaker to recuse himself from overseeing the Special Counsel Investigation".
FILE - Matt Whitaker, then an Iowa Senate candidate, speaks during the Iowa Republican Party's annual Lincoln Day dinner in Cedar Rapids, Iowa, April 11, 2014.
Graham, after a meeting with Whitaker, said he was confident there would be no interference in the investigation and said he said he saw no need for Whitaker to recuse himself as Democrats have demanded, the spokesperson confirmed.
Because of his comments, opposition Democrats, and some Republicans, have called for Whitaker to recuse himself from oversight of the Mueller probe.
A team of investigators led by Mr Mueller is looking into whether anyone from Mr Trump's campaign colluded in the effort.
However, The Atlantic suggested that Trump's "specific" attacks on Mueller show that he is anxious about the outcome of the investigation.