This was one of Murdoch's strongest indications yet that he could walk away from his bid, which would probably send Dow Jones shares tumbling back to their price levels before the offer was made public, analysts have said.
A representative of the Bancroft family declined to comment. A Dow Jones spokeswoman was not immediately available.
Murdoch was in Poland to meet Prime Minister Jaroslaw Kaczynski and government officials ahead of the relaunch of a television station in which he has a significant stake.
Sources familiar with the matter told Reuters Tuesday that News Corp. had cleared a major obstacle to the $5 billion purchase of Dow Jones after the two companies agreed in principle on safeguards to the editorial independence of Dow Jones' news operations.
Murdoch, News Corp.'s chief executive, is building his own financial news channel for cable television, aiming to usurp General Electric's CNBC, which has a news partnership with Dow Jones.
The Bancroft family met Murdoch in early June and discussed a proposal to protect editorial independence, and the talks accelerated last week.
Some three dozen Bancroft family members control Dow Jones through a combined ownership of 64%of voting shares.
Murdoch is offering to buy the company for $60 per share, a 65% premium to Dow Jones' stock price before the company's disclosure of the bid at the beginning of May.