The sale would include the 20th Century Fox film studio and the Sky and Star satellite broadcasters in Europe and Asia.
Disney was left as the front runner after Comcast, the NBC owner, dropped out of the race on December 11.
According to the Financial Times, talks about the price were continuing on December 12.
CNBC reported that Fox and Disney were on a “glide path” for an announcement on December 14, according to people familiar with the negotiations.
The Murdoch family was said to favor a deal with Disney because it would rather be paid in the entertainment giant’s shares than Comcast stock.
A deal with Disney could also face fewer regulatory hurdles, although it is extremely unlikely to be waved through.
Also in question is what will happen to 21st Century Fox’s bid to buy the 61% of Sky that it does not already own.
The deal is already under scrutiny by the UK Competition and Markets Authority (CMA), which is expected to publish its provisional findings in January.
It is not clear whether Disney will continue with the takeover if it buys the 39% stake from 21st Century Fox as part of the wider transaction.
The assets being sold by Fox include its FX and National Geographic cable channels, 22 regional US sports networks and the company’s stake in the Hulu streaming platform in the US.
It would also add to Disney’s extensive movie and TV library, with movies such as Avatar and Deadpool, as well as small screen hits including The Simpsons and Modern Family.
The Fox broadcast network, Fox News and Fox Sports would remain under the Murdochs’ control.
As well as its film studio, Disney also owns the ESPN sports network and cable channels.
Rupert Murdoch’s decision to sell most of Fox has surprised many commentators given his desire to continually expand his media empire over the past five decades.
Talks were understood to have been held between the two companies in November but did not result in an agreement.
Shares in Disney rose 0.5% in New York on December 12, valuing the company at $162 billion, while 21st Century Fox added 1%, valuing it at $62.6 billion.
Fox shares have jumped by close to a third over the past three months.
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