The publisher said: "The board of directors, including representatives of the Bancroft family, will conduct further discussions with News Corporation relating to the proposal and will oversee the exploration of strategic alternatives."
Bancroft family representatives said that any transaction must include "appropriate provisions with respect to journalistic and editorial independence" of Dow Jones's news operations, which include The Wall Street Journal.
Rupert Murdoch, chief executive of News Corp, has already held meetings with members of the Bancroft family in an attempt to calm fears about its bid for the business, but it is believed that Murdoch could not agree to some of the guarantees of editorial independence being proposed by the Bancrofts for a deal to go ahead.
News Corp submitted its unsolicited bid in early May, which valued Dow Jones at $5bn, or $60 a share, representing a 67% takeover premium.
After this bid was rejected, Murdoch stepped up plans to buy the company by offering the Bancroft family seats on the News Corp board, and proposed the creation of an independent editorial board for The Wall Street Journal.
Subsequently, the Bancrofts met Murdoch to discuss terms of a takeover and talks have been ongoing.
The slow pace of discussions is said to have frustrated the Dow Jones board, which felt the family was jeopardising the negotiations. The board's move to take control of the talks is predicted to bring the publisher closer to a sale.
Separately, MySpace founder Brad Greenspan is leading an investment group that aims to take a non-controlling stake in Dow Jones.
Journal Investment Group, led by Greenspan, sent a letter to the Dow Jones board offering to purchase 25% of outstanding common stock at a price of $60 a share. JI proposed it would subsequently buy shares from any shareholders wishing to tender their shares for $60 each, until it had acquired an aggregate amount totalling $1.25bn.
This proposal follows revelations that the Financial Times owner Pearson held discussions with NBC owner General Electric about launching a counter bid for Dow Jones earlier this week.
It is understood that the proposed venture between Pearson and GE would involve them combining to bid for Dow Jones, with each holding an equal share of the business and the Bancroft family maintaining a high minority stake in the publisher.
But, according to reports, senior figures at Pearson have expressed reservations about acquiring The Wall Street Journal, fearing the effects of a substantial overlap in readership between the newspaper and the FT.