A spokesman for the CIA said it was not policy to discuss classified briefings, but added: "When a CIA unit brought this matter to Director Panetta's attention, it was with the recommendation that it be shared appropriately with congress.
"That was also his view, and he took swift, decisive action to put it into effect."
Under US law, the president is required to make sure intelligence committees are fully informed about covert operations.
The newspaper did not name its sources and said it had been unsuccessful in reaching Cheney for comment.
Cheney has been criticised in the past for supporting controversial interrogation techniques such as waterboarding (where a detainee is made to feel as if he is drowning), sleep deprivation, long periods of standing and exposure to cold.
Many critics have described the methods as being torture.
Eric Holder, the US attorney general is reported to be considering assigning a prosecutor to investigate interrogation techniques used on terrorism suspects by the government of George Bush, the former US president.
Such an appointment could lead to a criminal inquiry into the treatment of prisoners by the CIA following the 2001 attacks in New York.
The move is seen as being controversial as Barack Obama, the US president, had previously said he wanted to leave the issue "in the past".
An official from the US justice department said Holder planned to "follow the fact and the law".
Holder's decision is expected to be made in the next few weeks.