CNBC first reported the news, adding that Murdoch would be suggesting that his son James be named his successor, said the Hollywood Reporter.
The 84-year-old media mogul would continue to be executive chairman of Fox, with his son Lachlan becoming executive co-chairman.
An announcement about the restructuring is expected soon, but it's unclear if the change would take effect this year or at the start of 2016.
As part of the shake-up, Fox COO Chase Carey would step down from that role and take on an undefined, advisory role at the company through the end of his current contract in mid-2016.