"I think Mr Trump is, for whatever reason, either intimidated by Mr Putin, afraid of what he could do, or what might come out as a result of these investigations... It's either naivety, ignorance or fear in terms of what Mr Trump is doing vis-a-vis the Russians," Brennan said in an appearance with Clapper on CNN's State of the Union.
Clapper added that foreign leaders who roll out the red carpet for Trump are able to manipulate Trump.
"I do think both the Chinese and the Russians think they can play him," Clapper said.
Their comments came after Trump told reporters over the weekend that he had spoken with Putin again over allegations of Russian meddling in the presidential election and that the Russian president again denied any involvement.
"I really believe that, when he tells me that, he means it," Trump told reporters. "I think he is very insulted by it, which is not a good thing for our country."
Treasury Secretary Steve Mnuchin said on the same show that the criticism levelled against Trump's management of relations with Russia and China was "ridiculous".
Trump also took a swipe at Obama-era intelligence officials Brennan, Clapper and former FBI Director James Comey, calling them "political hacks" and questioning the findings of a US intelligence report that concluded that Russians sought to tilt the election in Trump's favour.
Facing sharp criticism, Trump walked back from some of those comments on Sunday, saying he has faith in the intelligence leaders he has hired.
Brennan on Sunday called Trump's criticism of him a "badge of honour", and Clapper suggested said Trump's denial of Russian interference in the election "poses a peril to the country".
When asked, Brennan declined to say whether he knows of any intelligence to suggest that the Russians have compromising or damaging information on Trump.
A dossier penned by a former British spy contains unverified claims that Russia does have embarrassing information on Trump.
Donald Trump reportedly asked Putin if there was election meddling
Donald Trump asked Russian President Vladimir Putin directly whether allegations of Russian meddling in last year's US presidential election were true, RIA news agency reported on Sunday.
While in Vietnam for APEC on Saturday Trump said he believed Putin's denial of the accusations despite the view of US intelligence agencies that Russian interference did take place. Trump later distanced himself from his remarks.
On Sunday, Trump was careful to make clear he sided with the intelligence agencies under his own leadership. He has previously called the allegations of election campaign collusion with Moscow a hoax.
According to RIA, Kremlin spokesman Dmitry Peskov, asked how Trump had raised the question about alleged Russian meddling, said: "In fact, Trump asked whether that information could be true, how true it could be, and President Putin, for his part, explained his position, which is that Russia did not interfere in any election and this could not be the case."
Putin also said he did not understand "the groundless statements on the issue being made in the United States", Peskov added.
The Russian issue has clouded Trump's first year in office.
Trump's initial comments on Saturday drew criticism at home because US intelligence agencies have long since concluded there was Russian meddling through hacking and the release of emails to embarrass Democratic candidate Hillary Clinton.
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