Rupert Murdoch's Twenty-First Century Fox is expected to make an aggressive case for merging with Time Warner during its quarterly earnings call on Wednesday, though people familiar with the company's plans have said it would not use that forum to raise its bid.
Time Warner is due to report its financial results on Wednesday as well, marking the first time executives from both companies will publicly speak since the offer was first revealed on July 16.
Read MoreTime Warnerrejected $80B offer from 21st Century Fox
It will be an opportunity for Time Warner Chief Executive Jeff Bewkes to defend his record for shareholder value. Fox's Chief Operating Officers Chase Carey and James Murdoch will have the chance to discuss the more than $1 billion in cost savings and powerful combination of cable networks and sports programming. It is unclear whether Rupert Murdoch, chairman and CEO of Fox, will make an appearance given the stakes.
It will be an opportunity for Time Warner Chief Executive Jeff Bewkes to defend his record for shareholder value. Fox's Chief Operating Officers Chase Carey and James Murdoch will have the chance to discuss the more than $1 billion in cost savings and powerful combination of cable networks and sports programing. It is unclear whether Rupert Murdoch, chairman and CEO of Fox, will make an appearance given the stakes.
Fox has offered to buy Time Warner for about $80 billion, or about $85 per share, in a mix of cash and stock. Time Warner turned it down, saying its plan to go it alone "is superior to any proposal" from Fox.
Read MoreKen Griffin givesbacking to Time Warner-Fox deal
Though Fox is expected to raise its offer it will not rise beyond the range of $90 to $95 per share, a person familiar with Fox told Reuters on July 25. The timing of another offer is unclear. Some analysts have said that an even higher bid would be needed to win over Time Warner management and shareholders.
A spokesman for Fox declined to comment.
A potential tie-up would create one of the world's largest media conglomerates, dominating content production with two major studios, a stable of cable networks like Fox News and TNT, broadcast networks and pay-TV channel HBO.
Faced with a rash of media distribution mergers, such as Comcast's proposed $45 billion takeover of Time Warner Cable and AT&T's $48.5 billion deal to buy DirecTV, programing creators are responding with their own potential deals to add clout for negotiations with cable and satellite distributors and new entrants like Netflix and Amazon.
Bernstein Research analyst Todd Juenger wrote in a note to investors on Friday that it would be in the interest of both companies to ink a deal. He and his team spoke to hundreds of Fox and Time Warner shareholders and concluded that "most people are supportive."
"To reject the $85 a share offer, you would have to believe that Time Warner would get to $95 a share on its own," he wrote. "We don't find very many people who think it will be easy to get there."
Read MoreHow Time Warner maywind up in Murdoch's clutches
A Time Warner spokesman declined to comment.
With a backdrop of a rebuffed deal, Time Warner will be on the hook to explain why it is better off going solo.
Time Warner has outpaced its peers with 15.2 percent earnings per share growth for the past 5 years, nearly double the median for its competitors, according to Thomson Reuters data.
"Can Time Warner demonstrate to shareholders that left alone, the value to shareholders would be meaningfully greater than the $85 bid on the table from Fox?" Alan Gould, managing director at Evercore Partners, asked in a research note.
For now, Gould pointed out that there does not seem to be an alternative bidder.
—By Reuters
Disclosure: Comcast is the owner of NBCUniversal, the parent company of CNBC and CNBC.com.