"We're giving it a lot of thought and a lot of examination," said Murdoch, head of Fox's parent company, News Corp.
Fox owned-and operated TV stations and affiliates (a total of 205, according to The Wall Street Journal) now generally air reruns of syndicated sitcoms from 11 to midnight that make them a lot of money.
So, Murdoch said, executives Peter Rice and Kevin Reilly need to "show us we can do it and be fairly confident of making a profit."
The 78-year-old media titan — whose conglomerate owns 20th Century Fox movie studio, the Fox network, Fox News Channel, satellite services in Britain and Asia and several newspapers including The Wall Street Journal and New York Post — said there have been some conversations with O'Brien's people, but no "real negotiations" have taken place.
Murdoch's comments echoed those that News Corp. Chief Operating Officer Chase Carey and Fox Television Stations boss Roger Ailes made to the Los Angeles Times last month about the chances of O'Brien being signed to a deal.
O'Brien opted to leave as host of NBC's The Tonight Show rather than move the franchise to a half-hour later and clear the way for Jay Leno's return to 11:35 p.m. from prime time.
"I'm sure we'd have difficult renegotiations," Murdoch said of trying to gain approval from affiliates to put O'Brien on the air.
He said there were "different opinions" at the network about moving forward — but, if it "could make a profit, we would do it in a flash."