The controlling shareholders of Dow Jones are seeking guarantees from News Corp of the continued independence of its newspaper Wall Street Journal.
The Wall Street Journal may well get a new owner
An agreement on this issue is crucial to the success of News Corp's bid for the Dow Jones media group, according to reports in the Wall Street Journal.
Rupert Murdoch's firm made a $5bn (£2.54bn) offer for the Dow in May.
The Bancroft family controls 64% of the Dow Jones voting rights and will ultimately decide its future.
Members of the family had initially resisted selling the Wall Street Journal owner, but appeared to change course by holding talks with Mr Murdoch last week.
The US newspaper reported that the new terms of any potential deal - expected to be sent to News Corp - will include the appointment of a special autonomous board set up to safeguard the editorial independence of the Wall Street Journal.