According to the document, the investigation did not find any evidence of collusion between Russian Federation and Trump's campaign team.
Amid a broad effort to discredit Special Counsel Robert Mueller and the FBI, Trump and his allies have accused law enforcement officials of spying on his campaign and called for an investigation into the origins of the Mueller probe, which started at the FBI in mid-2016.
The inquiry, which will focus on whether the government's methods to collect intelligence relating to the Trump campaign were lawful and appropriate, is separate from an investigation by the Justice Department's inspector general.More news: Tim Conway, ‘Carol Burnett Show’ star, dies at 85
Several other media outlets also reported Durham has been tapped to lead the inquiry.
"I didn't know, but I think it's a great thing that he did it", Trump told reporters on Tuesday.
As he prepared to depart the White House on Tuesday, Trump was asked whether he retained confidence in Wray, given his answer.More news: Salah enjoys Premier League Golden Boot win
"That's not the term I would use", said Wray, a Trump appointee who took over leadership of the Federal Bureau of Investigation in 2017.
In a speech in Baltimore Monday evening, former deputy attorney general Rod Rosenstein said he believed the investigation "was justified, and closing it was not an option".
In 2017, former Attorney General Jeff Sessions assigned Utah's top federal prosecutor John Huber to review a wide range of issues that Republicans had complained about, from how the FBI handled investigations related to Democratic presidential candidate Hillary Clinton, to questions about the origins of the Russian Federation probe.
He had 18 people that didn't like Donald Trump that were Hillary Clinton fans.More news: Meghan, Prince Harry release baby feet photo for Mother's Day
Durham is a career prosecutor who was nominated for his post as US attorney in CT by Trump. He has previously investigated law enforcement corruption, the destruction of Central Intelligence Agency videotapes and the Boston FBI office's relationship with mobsters.