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 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."
The company – which includes the Fox Hollywood studios and television entities – was created two years ago when Murdoch broke off the struggling publishing operations of his News Corporation empire from the faster-growing media and entertainment operations.
He and his family remained in control of both companies after the split. The Australian-born Murdoch is executive chairman at News Corporation with his son Lachlan listed as co-chairman.
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