Washington DC - The FBI has opened a criminal investigation into its former director James Comey and ex-CIA chief John Brennan, two prominent critics of President Donald Trump, US media reported.

Fox News Digital said the probe involved "potential wrongdoing" related to the investigation into claims of Russian interference in the 2016 election won by Trump and alleged false statements made to Congress.

CIA director John Ratcliffe, a Trump appointee, had referred "evidence of wrongdoing by Brennan" to FBI director Kash Patel, another Trump appointee, for potential prosecution, Fox News Digital said, citing Justice Department sources.

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Comey and Brennan were named to their respective positions as head of the FBI and CIA by Democratic President Barack Obama, and they have a contentious history with Trump dating back to his first term in the White House.

Trump fired Comey in 2017 as the FBI chief was leading a probe into whether any members of the Trump campaign had colluded with Moscow to sway the 2016 presidential vote between Trump and Democratic candidate Hillary Clinton.

That investigation was taken over by special counsel Robert Mueller, who found there had been interference by Russia in the 2016 election in favor of Trump.

But Mueller said the probe "did not establish that members of the Trump Campaign conspired or coordinated with the Russian government in its election interference activities."

Trump revoked Brennan's security clearance in 2018, accusing the former CIA director of making "unfounded and outrageous allegations" about his administration.

The Justice Department declined to confirm the opening of a probe into Comey and Brennan.

"We do not comment on ongoing investigations," a spokeswoman said Wednesday.

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But White House Press Secretary Karoline Leavitt, asked about the report in a Fox News Channel interview on Tuesday evening, said she was "glad to hear it."

"Both of these disgraceful individuals turned against our constitution and our country," Leavitt said. "And I'm sure they did, in fact, lie to Congress.

"And it's up to the Department of Justice to investigate that and to prosecute them if they did," she said.

Since taking office in January, Trump has taken a number of punitive measures against his perceived enemies, stripping former officials of their security clearances and protective details, targeting law firms involved in past cases against him, and pulling federal funding from universities.