Clapper told a cyber-security forum in Washington Wednesday that the FBI and Department of Homeland Security were trying to "educate" campaign teams to better fend off hackers.
Clapper's office reported earlier this month that "like no other " foreign intelligence services had tracked the 2008 president election race, which involved the eventual Democrat winner Barack Obama and Republican senator John McCain."
"We'll probably have more," Clapper told Wednesday's meeting at Washington's Bipartisan Policy Center, without naming names. "We've already had some indications."
In 2012, the website of Obama's then-rival Mitt Romney was briefly shut down by cyber intruders.
In the past, US intelligence officials have blamed cyber intrusions on Chinese hackers.
"We're aware that campaigns and related organizations and individuals are targeted by actors with a variety of motivations - from philosophical differences to espionage - and capabilities - from defacements to intrusions," added Clapper's spokesman, Brian Hale
Campaign team security had not improved significantly since 2008, added Jonathan Lampe of the private information security company InfoSec based in Chicago.
Referring to Democrat Clinton's campaign team, Lampe said its websites were "open enough" back in October for anyone to grab data and use it.
Trump's team probably had the largest "attack surface" of all current candidates, said John Dickson, a San Antonio developer of software security.
"If it's the Bernie Sanders campaign, it's probably one website. If it's Donald Trump, it's his entire empire," said Dickson.
"This of the Chinese, Think of the Iranians. They have the intelligence capabilities, obviously, and maybe even the desire to disrupt elections," Dickson speculated.
"These campaigns are not working on encrypted platforms," added V. Newton Miller, the head of a Milwaukee-based encryption firm.
Hackers were especially interested in "sensitive information," rather than cyber vandalism, Miller said.
Associated Press said the Trump and Clinton campaigns did not respond to its questions about cyber-security.
Last year, Sanders fired a data director and apologized after Clinton's campaign alleged that information about potential voters had been stolen.
Clapper's spokeman Hale said questions on specific hacking incidents were better answered by the FBI.
ipj/bw (AP, AFP)