U.S. President Donald Trump's choice for attorney general, William Barr, said in a memo earlier this year that part of Justice Department special counsel Robert Mueller's investigation is "fatally misconceived," The Wall Street Journal reported on Wednesday.

The comment was made in a 20-page "unsolicited memo" dated June 8 to the Justice Department, according to the report, which added that the Journal had reviewed the document. Mueller is charged with investigating whether there are any links between Trump's 2016 presidential campaign and Russia as well as "any matters that arose or may arise directly from that investigation."

Barr wrote in the memo that he was concerned about Mueller looking into whether Trump obstructed justice in several incidents involving former FBI Director James Comey, according to the Journal. Comey claimed that, before he was fired by the president, Trump suggested he drop an investigation into former national security advisor Michael Flynn.

Flynn has pleaded guilty to lying to federal agents about his conversations with Russia's then-ambassador to the United States, Sergey Kislyak, in the weeks before Trump took office

Barr argued that Trump was acting well within his executive-branch authority, based on the facts as he understands them, the Journal reported. He said the inquiry into whether Trump obstructed justice is based on a "fatally misconceived" theory that could damage the presidency and the executive branch, according to the report.

The Justice Department did not immediately respond to CNBC's request for comment outside of U.S. business hours. It told the Journal that Barr wrote the memo "on his own initiative," according to the report.

Barr served as attorney general from 1991 to 1993 under President George H.W. Bush. Trump said earlier this month he will nominate Barr into the position. If confirmed by the Senate, Barr would take over from Acting Attorney General Matt Whitaker, who has been in that temporary role since Jeff Sessions left last month.

The Journal's report on Wednesday is not the first time Barr's criticisms on Mueller and his team have come to light. In a July 2017 report by The Washington Post, Barr raised questions about those in Mueller's team who have donated to Democratic candidates.

For the full report on William Barr's memo to the Justice Department, read The Wall Street Journal.