It’s a foregone conclusion now that something big will happen with Time Warner. Its stock wouldn’t be up 20% since yesterday morning — when Fox CEO Rupert Murdoch‘s $80B June offer came to light — if investors thought that Time Warner’s rejection of it was the last word on the matter. Indeed, the stock closed today at $86.12, which means a lot of people are betting that Fox or someone else will top the $85 a share stock-and-cash proposal that Time Warner shunned.

But here’s the problem: Some of Wall Street’s top analysts don’t know who has the desire and wherewithal to wage a bidding war with Fox. If Time Warner seriously wants to escape Murdoch’s embrace, it might have to make a deal of its own — perhaps to buy CBS. Even if it did, “Time Warner would still have to make the argument that more value would be created by merging with CBS than by accepting Fox’s tender offer,” Bernstein Research’s Todd Juenger says.

What about other usual suspects who might covet Time Warner? Comcast and AT&T are out of the running as they pursue their acquisition deals with, respectively, Time Warner Cable and DirecTV. Here are others that might conceivably kick the tires:

Disney: Hard to find anyone who thinks the company will jump in. Disney doesn’t need a big deal, especially with a “clear strategy that should play out over the last two years of Bob Iger’s contract,” MoffettNathanson Research’s Michael Nathanson says. The CEO likes properties that appeal to targeted audiences that he can coax to attend Disney theme parks or buy its merchandise. While he might make good use of particular Time Warner properties, including HBO and perhaps the DC Comics franchises, most of the other assets would add little to the Disney brand.

Janney Capital Markets’ Tony Wible says he’s “skeptical of a deal as we do not see all the various brands meshing well together given that [Time Warner] has some edgier content and [Disney] shareholders may resent using its cash to buy assets rather than returning capital to shareholders.” What about TNT’s sports rights with NCAA, MLB, and NBA? Probably overkill for ESPN. Pay TV distributors would take out torches and pitchforks if they thought that the most expensive basic cable channel might seek even higher prices to pay for additional sports costs.

Apple: The technology company doesn’t do content and, more importantly, loves generating high profit margins. They could be jeopardized if Apple spent $80B+ for Time Warner. It “would potentially limit content from other vendors” to iTunes and devices including Apple TV, BMO Capital Markets’ Keith Bachman says. And it would be counterproductive to blow up the models that make Time Warner’s cable channels, movies and TV shows so successful by distributing them on the Internet.

Facebook: On the plus side, Time Warner could produce a lot of premium online video for the social network company, which would open an opportunity for it to rival YouTube, AOL and Yahoo in video ad sales. But does Facebook really need to go through the trouble of buying an entertainment giant to accomplish that limited goal?

Google: YouTube could use more premium content — the kind of fare that doesn’t make advertisers cringe. And everyone’s waiting for the search colossus to buy an entertainment company that could feed YouTube, its Google Play store, Google Fiber, and any number of other initiatives.

Still, BMO Capital Markets’ Daniel Salmon doubts that Google would go after Time Warner “largely because it would not be aligned with the ‘long game’ we believe the founder-controlled company is playing to build more direct connections between content creators and users.” Chief Business Officer Nikesh Arora told analysts in a call today that Google has “lots and lots of content. Our monetization model is working.”

Verizon: The telco wants to become a video power. Verizon FiOS has 5.3M video subscribers. CEO Lowell McAdam talks openly about his interest in creating a wireless video service. Early this year the company bought Intel’s OnCue streaming platform. And it still has its Netflix-like Redbox Instant partnership. Verizon doesn’t want to be left behind as its top rivals — Comcast, Time Warner Cable, AT&T, and DirecTV — bulk up.

But Verizon’s primarily a wireless provider that may face additional competition if Sprint merges with T-Mobile. Instead of buying Time Warner, the telco likely is “saving some cash for upcoming spectrum auctions,” says Wells Fargo Securities’ Marci Ryvicker. Bernstein Research’s Paul de Sa also notes that Verizon, Comcast and AT&T typically “do not go into head-to-head price wars that suck value out of the industry. They tend to compete in what we call ‘bounded competition’ that retains sector profitability.”