Los Angeles Times, showing Mahony and other church leaders discussing ways to cover up alleged crimes by priests in California in the late 1980s.
In 2007, the archdiocese under Mahony, reached a USD 660 million settlement with about 500 alleged victims.
This month, files on more than 100 clerics accused of child sex abuse dating back to the 1980s, were released by the Los Angeles archdiocese.
This is while Mahony is still part of the 117-member conclave expected to meet in the Sistine Chapel until a new pope is selected.
The 85-year-old Pope announced his decision to resign on February 11. He will officially step down on February 28.
An association of Catholics in the US state of California have voiced opposition to a retired cardinal taking part in the conclave expected to vote for a successor to Pope Benedict XVI.
Catholics United has launched a petition against Roger Mahony, 76, from Los Angeles, who was stripped of church administrative and public duties for mishandling child sex abuse claims against tens of priests.
"If a Cardinal is stripped of public ministry in his diocese, why should he be rewarded with being allowed to vote for the next pope?" Catholics United asked.
On January 22 records were also released by