Fox COO Chase Carey would step into an advisory role as part of the generational shift at the parent of Fox News and the movie studio behind "X-Men" and other series, the source said, adding that James Murdoch and his 43-year-old brother Lachlan would work as partners.
It remained unclear what exactly that meant. Lachlan is currently non-executive co-chairman of the company's board. The elder Murdoch, whose media career spans the better part of a century, would become executive chairman, according to published reports.
Fox said Thursday it will take up the succession issue at its next board meeting. It was not immediately clear when the next meeting would take place.
The handing over of the reins has been widely expected on Wall Street. Shares of Fox were down about 1 percent in midday trading.
CNBC reported earlier that the elder Murdoch would still have the final say in whatever goes on at Fox. It was unclear whether the reorganization would take place this year or at the start of 2016, CNBC said.
"The most important thing in the immediate term is that Chase Carey not leave,” said Needham & Company Inc analyst Laura Martin. "Wall Street really cares about Chase Carey running this business. So if the implication of Rupert handing the title to his son is that Chase Carey leaves in the near term, we would expect that to negatively impact the stock prices."
As of April, the Murdochs owned 39 percent of voting shares in both Fox and News Corp, their empire's print arm, which operates newspapers like The Wall Street Journal and book publisher HarperCollins, through a family trust. Fox split from News Corp in 2013.
A Harvard University dropout, James spent his early career as a cartoonist and co-founder of hip hop label Rawkus Records, which was bought by News Corp. He joined News Corp in 1996 at 23 and soon ran the company's Asian assets. He was later named CEO of BSkyB, now known as Sky, that is 39 percent owned by Fox.
Some key investors have been warming to the idea that James has the ability to run Fox, describing him as curious and a risk-taker like his father. But they also cite two big differences that they like: James is less sentimental about certain assets than his father and he is more enthusiastic about courting shareholders.
The reported executive moves were not surprising - but their timing is, said Cowen & Co analysts in a note to clients, noting that Fox could soon cut earnings estimates. That could set a new, lower bar for a new CEO to target.
"We have always viewed Rupert as an empire builder who is more concerned with accumulating assets than with delivering shareholder returns, highlighted most recently by the aborted attempt to take over Time Warner," the Cowen analysts said.
Time Warner thwarted an $80 billion advance by Fox last year, in part by denigrating the non-voting stock that he was offering.
Fox shares were down 0.95 percent at $32.65, while News Corp shares were off 0.20 percent at $14.62 in afternoon trading on the Nasdaq.