Talks between the two began several weeks ago but fizzled due to disagreements over price, according to the newspaper.
Fox and WSJ parent News Corp share common ownership in the family-led empire created by mogul Rupert Murdoch.
Other companies such as Comcast, Verizon and Japan’s Sony have also expressed varying levels of interest, the report added, citing people familiar with the matter.
The discussions are focused on the Twentieth Century Fox movie and TV studio, some international assets like Fox’s 39 percent stake in British satellite TV operator Sky, India’s Star TV, and some US cable networks — but not Fox News — long seen as a jewel in the Murdoch family crown.
Disney is interested in solidifying its Hollywood and television positions and getting the Fox library of content to bolster its arsenal against Netflix and other rivals.
Disney, which owns the ABC television network, ESPN and has major studios in Hollywood, is set to launch its own streaming services aimed at competing against Netflix, Amazon and Hulu.
The news comes as another major media deal, between AT&T and Time Warner, has been challenged in an antitrust filing by the US Justice Department.
The rise of streaming services and the so-called cord-cutting movement against cable television, together with declining advertising revenue, have contributed to a rapidly changing landscape for media companies.