The US Justice Department has launched a criminal investigation into the origins of the Mueller inquiry, US media report.
An administrative review into the Special Counsel's investigation began in May.
But the switch to a criminal probe means investigators can now issue subpoenas for testimony and documents.
President Trump has long alleged Robert Mueller's probe of reports of collusion with Russia was a "witch hunt".
The investigation into the 2016 election did not establish any criminal conspiracy between Moscow and Donald Trump's campaign. But it did not clear the president of obstructing justice.
Mr Durham was tasked with determining whether the collection of intelligence on the Trump campaign in 2016 was lawful. He is known for investigating links between FBI agents and organised crime, and investigating the destruction of CIA interrogation videos.
Last April, Mr Barr told members of Congress that he believed "spying did occur" on the Trump campaign in 2016, adding: "The question is whether it was adequately predicated. And I'm not suggesting that it wasn't adequately predicated. But I need to explore that."
BBC
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Donald Trump has confirmed that he will not take part in Republican presidential debates with his rivals in the race for the White House.