The News Corporation has made a $5 billion (£2.5 billion) bid to take over Wall Street Journal owner Dow Jones.
The company behind Rupert Murdoch's vast global media empire confirmed in a statement that it had made a "friendly offer" of $60 (£30) per share for the publishing group.
News Corp said it was also prepared to offer a combination of cash and its own stock to secure control of Dow Jones.
But while yesterday's bid represents a premium of around 65 per cent to Dow Jones' closing share price on Monday, the family which owns the majority of the company's shares has indicated it will harness its influence to reject the deal.
Dow Jones confirmed late yesterday that a representative of the Bancroft family had informed its board that they intended to vote shares representing just over 50 per cent of the company's voting power against the proposed offer from News Corp.
The board of Dow Jones are currently considering the proposal, which could result in a higher offer from Mr Murdoch's media company if it is rejected.
Responding to news that the Bancrofts might vote against the News Corp bid, Mr Murdoch told his own Fox News Channel that he hoped the family would consider the offer. He stressed there was "plenty of time" for a deal to be made.
In an interview for the channel's Your World with Neil Cavuto programme, Mr Murdoch also insisted that News Corp would be "great guardians" of the Wall Street Journal and would be able to help boost its circulation.
Analysts say that a successful News Corp take-over of the respected title would be a coup for Mr Murdoch ahead of the forthcoming launch of the company's new Fox Business Channel.
But the union representing Dow Jones workers said that it opposed the bid and claimed a merger with News Corp would threaten the company's editorial independence.
"Mr Murdoch has shown a willingness to crush quality and independence, and there is no reason to think he would handle Dow Jones or the Journal any differently," the Independent Association of Publishers' Employees said in a statement.