The report, citing "numerous sources close to the Murdoch family," said the 84-year-old tycoon would remain executive chairman of the group with his other son Lachlan as co-chairman in the move this year or in early 2016.
The company did not immediately respond to an AFP query on the report.
The report said James Murdoch, 42, would take over day to day management at Fox, working "in tandem with his 43-year-old brother Lachlan and his father."
He and his family remained in control of both companies after the split. The Australian-born Murdoch is executive chairman at News Corp. With his son Lachlan listed as co-chairman.
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Rupert Murdoch has spent a lifetime building his News Corp empire from a single Australian newspaper he inherited.
The success of his London-based newspapers helped finance his 1981 purchase of The Times and Sunday Times, both prestigious broadsheets, in an acquisition that met with intense opposition from parts of Britain's establishment.
He relocated to the United States where more bold acquisitions followed and where he became a naturalized US citizen in 1985.
The empire came under pressure in recent years from the slump in newspaper revenues, and a scandal in Britain which led to the shutdown of News of the World after the revelation the tabloid hacked into the phones of a murdered teenager and the families of dead soldiers.
In the latest quarter, Fox reported net income of $975 million on revenues of USD 6.5 billion. The company includes the Fox studios in Hollywood and a global array of cable and broadcasting operations, including the Fox television entities, National Geographic Channels and local television stations, along with a stake in the Sky satellite television service.