Multiple legal and constitutional scholars have argued that Whitaker's appointment to acting attorney general was unconstitutional because he was not confirmed to the position by the US Senate.
Barr previously served as attorney general from 1991 to 1993 under President George H.W. Bush and is highly respected in the conservative legal world.
Nadler said he might need the "threat" of the subpoena to get answers during the Friday session.
Barr said he takes seriously the department regulations that say Mueller's report should be confidential. "I hope and expect he will be confirmed next week".
To date, the committee has interviewed more than 200 witnesses and reviewed more than 300,000 pages of documents; it has held more than a dozen public hearings and released two interim reports, CBS News reported.
Gillibrand Supports Woman Who Accused Virginia Lt. Gov. Fairfax Of Sexual Assault
While both sides are now being hit, the controversy kicked off last week when Democrats called for the resignation of Gov. Ralph Northam over a racist photograph featured on his personal page in his 1984 medical school yearbook.
Attorney General nominee Bill Barr meets with Sen.
Barr pledged at his confirmation hearing to keep politics out of Justice Department decisions and said he would refuse an instruction from the president to fire Mueller absent good cause to do so.
But Democrats said Thursday that Barr's comments did not go far enough to reassure them.
Whitaker, who was appointed by Trump in November, said last week that the investigation "is close to being completed". That, combined with Barr's sweeping view of executive power, prompted Leahy to vote no on Barr's nomination.
Trump had repeatedly criticized Sessions for recusing himself from Mueller's investigation into Russian interference in the 2016 presidential election that includes examining the ties between Russia and the Trump campaign.
Barr broke with Trump in saying, "I don't believe Mr. Mueller would be involved in a witch hunt", a term Trump frequently used to decry the probe. But Grassley said he would support Barr's nomination, despite his reluctance to commit to releasing Mueller's findings.