Snowden, now living under asylum in Russia, left the CIA and became a contractor for the National Security Agency. This summer he leaked thousands of classified documents on the NSA's covert programs to spy on telephone calls and Internet traffic at home and abroad.
The supervisor's note and the CIA's suspicions do not appear to have been forwarded to the NSA, the Times said.
They surfaced only after investigators started probing Snowden's records once he began to spill the beans on the surveillance programs, the paper said.
In the derogatory report on Snowden, the supervisor wrote that he had detected a distinct change in the computer technician's behavior and work habits, the paper said.
That report and the CIA's suspicions may have been the first warning of what Snowden might have in mind for the future, and a chance to review Snowden's top-secret clearance or put his work at the NSA under closer surveillance, the paper said.