US media suggests Disney does not want to be associated with the media mogul's highly partisan, right-wing Fox News network.
However, Disney has not clarified its reasons.
It bought the studio, with other media operations, in a $71bn deal last March.
20th Century Fox is known for producing some of the biggest films of all-time, including Avatar and Titanic.
Hollywood is known for being liberal, unlike the Australian tycoon.
Disney has also renamed Fox Searchlight Pictures, the arthouse arm, as simply Searchlight Pictures.
