Michael Elefante, a representative of the Bancroft family, which controls 64.2% of the voting shares, said that representatives of the family would meet Rupert Murdoch, chief executive of News Corp, to discuss issues related to journalistic integrity raised by News Corp's bid.
Elefante said: "After a detailed review of the business of Dow Jones and the evolving competitive environment in which it operates, the family has reached consensus that the mission of Dow Jones may be better accomplished in combination or collaboration with another organization, which may include News Corporation."
But Elefante said that there was no assurance the discussions would lead to a proposal satisfactory to members of the family.
He added: "The family also indicated its receptivity to other options that might achieve the same overarching objective."
Following the Bancroft's decision, the Dow Jones board stated it would consider News Corp's offer, as well as other approaches.
On Wednesday this week, the largest non-family shareholder in Dow Jones, publisher of The Wall Street Journal, called for the Bancroft family to sell their controlling share to News Corp.
Brian Rogers, the chairman and chief investment officer of investment firm T Rowe Price, which holds about 15% of Dow Jones or 4.5m shares, said the family had no plan in place to lift the company's share price to the level offered by News Corp.
Murdoch's takeover offer, which was rejected in early May, valued Dow Jones at $5bn, or $60 a share, which represented a 67% premium.
Following the rejection, 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.
Some members of the Bancrofts stated that they refused to sell the company to Murdoch at any price, concerned that a News Corp takeover would "crush quality and independence" at the journal..jpg)
.jpg)