The Bancroft family, which controls media group Dow Jones, has held "productive" discussions about selling the firm to Rupert Murdoch's New Corp.
The Bancroft family has controlled Dow Jones for more than 100 years
Following a meeting in Boston, the family may make a decision on the $5bn (£2.5bn) offer by the end of the week.
Winning over the Bancrofts - who hold 64% of the firm that owns the Wall Street Journal - is the key hurdle Mr Murdoch must clear to buy Dow Jones.
The Dow Jones board gave a tentative approval to the deal last week.
If the takeover does go ahead, it could reshape the US media landscape.
A successful bid would bring Dow Jones publications into the same stable as News Corp's New York Post in the US, and the Sun and the Times in the UK.
Following the meeting, the Bancroft's family trustee, Michael Elefante, issued a statement describing the discussions as ""very productive".
Family members and trustees "now have all the information they need to make informed decisions about the News Corp proposal", he added.
However, while the company's board has backed the bid, many unions, journalists and even one executive have voiced their opposition to the move.
Dissenters have voiced concern that a takeover could affect the journalistic independence of the firm, and that Mr Murdoch may interfere in the running of the Wall Street Journal.
Last week, the company's German director Dieter von Holtzbrinck quit the Dow Jones' board saying he was "very worried" about the impact of the bid on the Wall Street Journal.