"We already have some indications of that," he said during a cyber-security discussion at the Bipartisan Policy Center in Washington.
"I anticipate that as the campaign intensifies, we are probably going to have more of it."
The Department of Homeland Security and the Federal Bureau of Investigation are doing "what they can" to educate both campaigns against potential cyber threats ahead of the general election in November, when Republican Donald Trump will likely face off against Democrat Hillary Clinton, Clapper said.
Asked for details about specific incidents, Clapper's office referred questions to the FBI.
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"We're aware that campaigns and related organizations and individuals are targeted by actors with a variety of motivations -- from philosophical differences to espionage," FBI spokesman Brian Hale later said.
Those attacks ranged from "from defacements to intrusions," he added. The FBI did not immediately respond to a request for additional details.