Representatives of the Bancroft family, which controls Dow Jones
The meeting is expected to deal solely with issues related to journalistic integrity, these people said, according to the Journal.
The Journal also reported that Michael Elefante, a partner at the law firm that represents the Bancroft family, has changed his mind about considering selling Dow Jones, the Journal reported.
Elefante now has said the company should consider a sale to Murdoch or another bidder in order for the media company to remain competitive, the Journal reported, citing sources.
On Friday, shares of Wall Street Journal publisher Dow Jones jumped above News Corp.'s $60-a-share bid for the first time as investors bet a better offer could emerge.
The stock rose as much as 15% after the Bancroft family, which holds 64% of voting power in Dow Jones, said late Thursday that it would consider News Corp.'s $5 billion bid, as well as other offers.
The statement raised expectations that News Corp. Chairman and Chief Executive Rupert Murdoch might sweeten his offer to clinch the deal, and stoked hopes that other parties could bid for part or all of Dow Jones.
Investors and Wall Street analysts have said Murdoch could raise his bid to $70 a share or more, which would approach Dow Jones stock's all-time high of $77.31 on June 20, 2000.
The Bancrofts' decision to meet with Murdoch marks a sharp change from their previous outright opposition to a sale to News Corp. The family said it would seek a commitment from Murdoch to preserve the editorial independence of Dow Jones after a sale.
News Corp.'s offer was a 65% premium to the share price before the bid became public last month, a value many outside shareholders found persuasive despite concerns that Murdoch could hurt the Journal's reputation or interfere in news reporting.
Despite its expansion into digital publishing, Dow Jones is suffering from a slowdown in advertising sales, as advertisers and readers shift their attention to the Internet.
Besides The Wall Street Journal, Dow Jones publishes investors' newspaper Barron's, news Web site Marketwatch.com, and Dow Jones Newswires, which competes with Reuters Group in publishing financial news.
The proposed Thomson-Reuters merger also has put pressure on the Bancrofts to sell Dow Jones as the market for financial news and information consolidates.
But analysts question whether other media companies or private equity firms would top Murdoch's offer.
For now, Bloomberg, rumored in the press to be a potential bidder, has ruled out the option.
"We are not pursuing acquisitions at this time," a Bloomberg spokeswoman said in an e-mail. "Bloomberg continues to focus on our continuing organic growth and serving our customers."