The memos were drawn up by Justice Department lawyers during the former administration of Geroge W. Bush and if published would set out details of interrogation techniques of terrorist suspects for the first time.
"(The memos)… provide the legal rationale for waterboarding, head slapping and other rough tactics used by the CIA," Newsweek reported.
The move would follow the publication earlier this month of nine Bush-era memos and opinions it said gave legal grounding to the controversial policies.
The nine documents — the first dating from the wake of the September 11, 2001 attacks to the last from the months following the US-led 2003 invasion of — detail how Bush gave himself sole power over terror suspects.
Those documents were released as President Barack Obama’s administration vowed to end the use of controversial tactics, such as waterboarding, which it has called torture.
"Waterboarding is torture," Attorney General Eric Holder said. "The use and sanction of torture is at odds with the history of American jurisprudence and American values."
According to Newsweek, some in the intelligence community continue to oppose the publication of the three most recent memos, arguing that they could give enemies an insight into US aims and strategies.
The publication of the documents is likely to fuel calls to establish a commission to investigate the Bush administration’s prosecution of the war on terror.