Rock, 63, was arrested at his home in London in February after Downing Street officials contacted officers.
He was questioned by investigators from the newly formed National Crime Agency (NCA), the BBC reported.
Rock was deputy head of Cameron's policy unit at the time of his arrest and they have known each other since the late 1990s, the report said.
They worked together as special advisers.
At the time of his arrest, the NCA said Rock was detained on suspicion of an offence "relating to child abuse imagery".
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Questions were raised about the manner in which the police came to know.
Cameron said he was "told about this issue pretty much as soon as it was discovered".
The arrest was not made public until details were published in a newspaper three weeks later.
Rock failed to win a seat in Parliament on three separate occasions in the late 1970s and early 1980s.