Bolton was in Israel for the first time as a Trump administration official to discuss national security issues with Prime Minister Benjamin Netanyahu and other top officials.
"In terms of what [Brennan] said, since he left, a number of people have commented that he couldn't be in the position he is in, criticizing Trump, unless he did use classified info," Bolton told ABC's "This Week" on Sunday. "I don't know specifics, but I do know when he was [CIA] director, I was troubled by comments in public, and the politicization."
"My opinion is that he was politicizing intelligence," Bolton added, saying Brennan had failed to keep intact the "wall of separation between intelligence and policy."
Host Martha Raddatz ultimately asked him, "You’re not sure whether John Brennan used classified information? You have no specific examples."
Bolton replied, "I think a number of people have commented that [Brennan] couldn’t be in the position he’s in of criticizing President Trump and his so-called collusion with Russia unless he did use classified information. But I don’t know the specifics."
President Trump revoked Brennan's security clearance on Wednesday, saying he had politicized his security clearance and misled Congress about CIA spying in the Senate.
A broader review of who can retain security clearances after leaving the federal government may be warranted, Bolton added.