Shares in the Dow Jones media group have jumped on hopes that a takeover battle could break out for the firm.
Rupert Murdoch has pledged to protect the paper's independence
Earlier the Bancroft family, which controls the group, said it would consider selling Dow Jones to Rupert Murdoch's News Corporation.
But the family, which controls 64% of Dow Jones' voting rights, added it would also consider any rival offers.
News Corporation made its $5bn (£2.5bn) bid at the start of May, but the Bancrofts have not commented until now.
Shares in the group closed $7.89, or 14.8%, higher at $61.20 on the US market - higher than the Murdoch offer of $60 per share.
Dow Jones owns the Wall Street Journal and other newspaper titles.
"The family has reached consensus that the mission of Dow Jones may be better accomplished in combination or collaboration with another organisation, which may include News Corporation," the Bancrofts said in a statement.
With the family said to have been originally concerned about the ongoing reputation of the Wall Street Journal, they added that they would meet Mr Murdoch to see if they could find a way to protect its editorial independence after any sale.
Their comments come two weeks after Mr Murdoch reached out to the family in a letter published in the Journal.
In the letter Mr Murdoch said he would establish "an independent, autonomous editorial board" for the newspaper.
He added that he would invite a Bancroft family member to join this board "to help alleviate any concerns about maintaining journalistic integrity and ensure good communication between the family and News Corporation going forward".
Analysts are divided over whether a rival bidder for Dow Jones may come forward.
While some think it is likely, others say News Corporation's offer price is too high for others to better.
The main US share index is named after the Dow Jones company.