According to The Wall Street Journal, Michael B Elefante, the family lawyer in charge of managing the vote, last night told the Dow Jones board that as it stood less than half of the family's 64% voting stake would be cast for the takeover.
However, some family members have yet to submit their votes and this has delayed the result, which was expected over the weekend. Elefante has given them a deadline of 5pm today (10pm UK time).
Murdoch's News Corporation needs family votes representing around 30% of the overall vote to ensure a comfortable majority in its favour. Non-family shareholders, accounting for 29% of the vote, are expected to support Murdoch.
The voting process has been complicated by the system of trusts which exist to steward the family shares.
Lawyers have found it necessary to dissolve one trust, which required a unanimous verdict in order to allow different beneficiaries to vote in different ways; this is expected to work in Murdoch's favour.
Further evidence of the divisions within the clan over the acceptability of Murdoch's ownership of the Journal have emerged in the last few days.
One of the elder members of the family opposed to Murdoch, Jane Cox MacElree, is reported by the Journal to have resigned from some of the trusts she oversees rather than risk litigation from their beneficiaries if she votes against a deal.
In contrast, her son Crawford Hill has backed Murdoch in an email to family members, calling his offer a "no-brainer".
He wrote: "[The offer is] a tremendous business deal for DJ shareholders and will take the business into the next successful phase in a manner not possible if DJ remains independent."
Another family member, William Cox Junior, is reported to have switched his position in the past few days and now favours the sale.
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