Rex Features
The former Tonight Show host, who recently departed the NBC network in controversial circumstances, has since been linked with a move to Fox.
The Wall Street Journal reports that Murdoch said on Tuesday there is "differing opinions within the network" on whether the proposed move makes financial sense.
The News Corp chairman also confirmed that there had been "no real negotiations" thus far, but "some conversations" about a new late-night show for O'Brien on Fox.
Murdoch added: "I'm sure we'll have some difficult negotiations."
