Cheney, who was vice-president in the administration of George W. Bush, has not commented on the allegations that he asked the spy agency to deliberately conceal its activities from the US legislature.
The details of the intelligence programme, launched after the attacks on the US on September 11, 2001, have remained secret, but The Wall Street Journal has reported that the programme was part of an effort to capture or kill al-Qaeda fighters.
Amid calls for an investigation into Cheney’s conduct, Senator Dick Durbin, a Democrat, said the former vice-president’s actions had been “inappropriate”.
“To have a massive programme that is concealed from the leaders in congress is not only inappropriate; it could be illegal,” he said.
A spokesman for the CIA said it was not policy to discuss classified briefings, but said: “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.
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 the Bush administration’s policy on using particular interrogation techniques against terrorism suspects.
Such an appointment could lead to a criminal inquiry into the treatment of prisoners by the CIA after the Septemeber 2001 attacks.
An official from the US justice department said Holder planned to “follow the fact and the law”.
Holder’s apparent move is seen as being controversial as Barack Obama, the US president, had previously said he wanted to leave the issue “in the past”.
A legal challenge against former members of the Bush administration could hamper efforts by Obama to push his legislative programme through congress.
While the Democrats have the outright majority in the senate, Obama campaigned for the US presidency on the promise that he would seek bipartisan accord when trying to pass legislation.
Holder’s decision on whether to appoint a prosecutor to investigate interrogation techniques used against terrorism supects is expected to be made in a few weeks.