Brennan has not only denounced Trump's tone and temperament but also his policy decisions, such as the president's decisions to withdraw from the Paris climate accord and Iran nuclear deal.
On Wednesday, Trump revoked Brennan's security clearance, which had allowed the ex-spymaster to continue to access classified documents since he resigned last January.
The current administration has questioned the loyalties of such officials, viewing their comments as attacks against the president, especially those focusing on the intelligence findings that Russian Federation intervened in the 2016 election won by Trump.
Press Secretary Sarah Sanders said in July that they had "politicized, and in some cases monetized, their public service and security clearances". "Mr. Brennan's lying and recent conduct characterized by increasingly frenzied commentary is wholly inconsistent with access to the nation's most closely held secrets and facilities".
In a highly unusually directive, Trump claimed that Brennan - a former station chief in Riyadh who rose to lead the formidable spy agency - had become "erratic".
Meanwhile, Benjamin Wittes of Lawfare said Comey told him he doesn't even have a security clearance to revoke and that he was "read out" when he left the government, which he said is normal practice. The White House later said the date was an error.
Mrs Sanders also denied that the move was being taken to punish Trump critics, saying it was to "protect classified information". "I don't think I can sign up to that", Clapper said.
Trump revoked former CIA Director John Brennan's security clearance Wednesday. Brennan's mentor, ex-CIA Director George Tenet, for example, had powerful Rabbis in President George W. Bush and Vice President Dick Cheney, as well as a bizarrely empathetic Establishment media, when Tenet quit in disgrace 2004.
United States media fight back against Trump attacks
Almost 350 newspaper and other organisations are thought to have published a co-ordinated series of editorials condemning the US President's attacks on "fake news".
The host asked Brennan if Trump was afraid of Russian President Vladimir Putin.
David Priess, a former career CIA analyst and daily intelligence briefer, told CBS News that "this is the first time I have seen or heard about something like this being done".
So Trump's public - and obviously jocular - expression of hope that Russian Federation might be able to "find the 30,000 emails that are missing" makes Brennan wonder what Trump privately encouraged his advisers to do.
He later tweeted "John Brennan is a stain on the Country, we deserve better than this", quoting the author of a new book that claims Trump's predecessor Barack Obama attempted to sabotage his presidential campaign.
The threat to pull his security clearance, Clapper added, will not silence him.
Rep. Nancy Pelosi, the House Democratic leader, said Trump's move was a "stunning abuse of power".
"I think he is dishonest, he lacks integrity, he has very questionable ethics and morality, and he views the world through a prism of 'how it's going to help Donald Trump?'" Brennan said in an interview with NPR's All Things Considered in April.