News Corp has said it is in talks with Rebekah Brooks after reports she will return as chief of its UK division.
The former News of the World editor quit as UK chief executive four years ago amid the phone-hacking scandal. She was later cleared of any wrongdoing.
Her re-appointment could be confirmed next month, the Financial Times said.
Campaign group Hacked Off said it was a sign of an "unreformed, unrepentant press", but a former Times executive editor said hacking was in the past.
Mrs Brooks edited both the Sun and the NoW in a long career at Rupert Murdoch's company.
She resigned as UK chief executive in July 2011 in the wake of the phone-hacking scandal at the NoW, which eventually closed the paper.
Royals, celebrities and victims of crime were among those whose phones were hacked by journalists at the Sunday tabloid.
Mrs Brooks had denied any involvement and was cleared of charges relating to phone hacking last year. Andy Coulson, another former NoW editor, was jailed after being convicted of conspiracy to hack phones.