The company has quietly put out feelers for a possible new head of Fox News with the preference, say sources, that it be a woman. The Murdochs may be preparing for a leadership change at Fox News. Sources tell The Hollywood Reporter that Rupert Murdoch and his sons James and Lachlan, CEO and co-chairman of Fox News parent 21st Century Fox, have quietly put out feelers for a new head of Fox News. And the preference, according to two sources familiar with the Murdochs’ thinking, is that the new leader be female.