Brooks, who formerly edited The Sun and The News of the World, resigned as chief executive in 2011 at the height of a scandal over the hacking of phone voice mails by journalists.
She was arrested on suspicion of being involved, but was cleared of all charges last year.
Speculation has grown in recent months that Brooks, 47, might return to the Murdoch empire.
Brooks was initially reluctant but was persuaded to take the chief executive job by the Australian-born business magnate, with whom she has a close relationship, the Financial Times reported citing people familiar with the matter.
The idea was criticised by campaign group Hacked Off, which represents victims of phone hacking.
"This is a major misjudgement of the public's mood by a company still ethically out of control," said joint executive director Evan Harris.
The report came as it emerged that Britain's Crown Prosecution Service (CPS) was considering bringing corporate charges -- meaning the prosecution of a company for wrongdoing -- over phone hacking at News of the World, which was closed in 2011 due to public outcry.
Police can bring charges against a company, just like they can against a person, because a company is a legal entity.
The newspaper is at the centre of a police investigation into phone hacking called Operation Weeting.
"We have received a full file of evidence for consideration of corporate liability charges relating to the Operation Weeting phone hacking investigation," CPS said.
In a statement, the Metropolitan Police said the file had been submitted last month.
"On the 23 July, following the investigation into phone hacking at the News of the World, detectives from Operation Weeting submitted a file to the CPS for their consideration," the statement read.
News Corp did not immediately respond to a request for comment from AFP.