Murdoch and his son James were in discussions with the Bancrofts, who own a 64% stake in Dow Jones & Company, for five hours yesterday in New York about News Corp's unsolicited bid, as they attempted to ease fears about the future and journalistic integrity of its flagship title, The Wall Street Journal.
Rupert Murdoch said he had a "long and constructive meeting", which was understood to have been attended by Christopher Bancroft, Leslie Hill and Elizabeth Steele, all directors at Dow Jones.
One of the key areas likely to have been discussed is the protection of the editorial independence and integrity of The Wall Street Journal -- an issue that Murdoch's critics said would be undermined if News Corps' bid were accepted.
However, according to reports in The New York Post, Murdoch would not accept the Bancroft's proposal to set up a board of independent directors to oversee all editorial senior appointments across the company.
Meanwhile, the Independent Association of Publishers' Employees, the union representing more than 2,000 Dow Jones workers, has said it wishes the company to seek alternative bids that would better serve the interests of The Wall Street Journal.
It is understood Steven Yount, union representative for Dow Jones & Company, has contacted around a dozen unnamed parties, which he believes have "the money and the integrity" to become potential buyers.
Further meetings between News Corp and the Bancrofts are expected to be held later this week.