It was apparently from the New York Times, quoted after his death, by an unnamed source:

And President Kennedy, as the enormity of the Bay of Pigs disaster came home to him, said to one of the highest officials of his Administration that he “wanted to splinter the C.I.A. in a thousand pieces and scatter it to the winds.”

Now, far be it from me to question the integrity of The Gray Lady, but this is about as loose of a quote on Kennedy as the one about Nixon actively seeking to target black people with anti-crime laws. (It was an alleged quote from Erlichman, several years after both Nixon and Erlichman were dead, after the author hadn't said a word nearly 9 years after the interview, and all of the surviving members of Nixon's cabinet denied it).

That being said, I'd bet that he was absolutely fucking pissed at the CIA failing as spectacularly as it did with the Bay of Pigs invasion. They were arrogant, a whole bunch of people got slaughtered, it became an international scandal, and Kennedy got blamed personally. That doesn't necessarily mean he wanted to dissolve the CIA. Think about how many people the FBI went after, and yet no one even made an attempt to break them up.

Considering all the other intelligence agencies that existed without public knowledge at the time, and that Kennedy was still happy to work with, I doubt that his attitude would be against dissolving the entire security state apparatus. At most it would be just re-organizing the CIA so it stopped fucking up and getting him in trouble.