The main union at the Dow Jones media group has claimed that billionaire investor Ron Burkle is now working with them to mount a rival bid for the firm.
The company owns the Wall Street journal
An official for the Independent Association of Publishers' Employees (IAPE) said it had also approached fellow US billionaire Warren Buffett.
The union's comments come as it opposes a $5bn (£2.5bn) offer for Dow Jones from Rupert Murdoch's News Corporation.
Neither Mr Burkle nor Mr Buffett has yet responded to the union's claim.
IAPE representative Steven Yount said Mr Burkle had told the union that he is interested in working with it to formulate an offer for the company, which owns the Wall Street Journal and other newspaper titles.
Mr Burkle tried to buy the Tribune group last year
Mr Burkle, who made his fortune in the supermarket sector, was part of an unsuccessful bid last year for rival publishing company Tribune.
Serial investor Mr Buffett said last month that it was "very, very unlikely" that he would bid for Dow Jones, either as a personal investment or through his company Berkshire Hathaway, due to Mr Murdoch's high offer.
The IAPE added that it was still keen to talk to any other interested parties.
Its comments came a day after Mr Murdoch held his first meeting with members of the Bancroft family, which controls 64% of Dow Jones' voting rights.
Both Mr Murdoch and the family said the talks were "constructive", but neither gave any more details, especially regarding whether the family was willing to sell.
Amid fears that Mr Murdoch will interfere in the running of the Wall Street Journal, he has already promised to establish "an independent, autonomous editorial board" for the newspaper if his bid for Dow Jones is accepted.
The main US share index is named after the Dow Jones company.