Twitter website on an iPhone (© Jonathan Hordle-Rex Features)
CNBC
By Alex Rosenberg

Apple (AAPL) shares got a boost this week after Carl Icahn revealed on Twitter that he had initiated "a large position" in the stock. In fact, from Icahn's Tuesday afternoon tweet to Apple's close that day, the company gained over $13 billion in market share. That's more than the estimated valuation of Twitter itself, which Greencrest Capital pegs at around $11 billion.

So given the power and reach of the social network, should Apple just go ahead and buy Twitter? Many have long suggested that they could make beautiful music together.

"Apple hasn't been able to do anything in social, and what Twitter does is put them in a scenario where they can start disseminating information -- because that's really what Facebook's (FB) business is, and Google's (GOOG)" said Dan Nathan of RiskReversal.com. "It would be a huge departure from Apple's history, but I think it makes a lot of sense."

"There's a lot of things they could do with Twitter," said Nathan, a contributor to CNBC's "Options Action." For instance, Apple has 575 million iTunes users, and there would be a lot of cross-selling opportunities.

The problem is that the tech giant may have missed the boat.

In April 2012, Ironfire Capital Founder & Managing Partner Eric Jackson made a strong case in Forbes that Apple should, and would, buy Twitter. But he no longer thinks it's feasible.

"I definitely think Apple should buy Twitter," Jackson wrote to CNBC.com. "However, I think that ship has sailed. The time to buy was a year ago. Twitter will probably IPO this fall," and "they'll want to see that through."

Max Wolff, senior analyst and chief economist at Greencrest Capital, is of a similar mind. "I would be surprised if Twitter didn't IPO by the middle of next year or sooner," he said. At this point, "I think that Twitter is big enough that they don't need an M&A exit."

In Wolff's view, an Apple acquisition of Twitter would be very strange.

"It sort of makes sense, because Twitter has really proven themselves in an area that has proved elusive for Apple," Wolff said. "However, it's a totally different business model."

In addition, "if you're Twitter, with 500 million users and 250 million active accounts, your growth has been in a non-Apple world. If Apple walls you off" by restricting Twitter to Apple devices, "you'll see a huge diminution in users."

And that would mean a serious reduction in Twitter's influence. "Twitter has become pretty powerful," Wolff said. "It's the first draft of history."

Rob Cihra, who covers Apple for Evercore Partners, doesn't see an Apple acquisition of Twitter happening anytime soon.

"I think it's one of those ideas that's floated because it could certainly make sense -- but so could a lot of things," he said. "Apple casts a pretty wide net, with hands in a whole lot of different markets, and products accessing different markets, and a whole lot of cash. You combine those, and most anything seems possible."

Apple's acquisitions have tended to be on the small side, and "I don't see any reason to expect them to do anything other than they've been doing," said Cihra, who has an "overweight" rating on the stock. "Apple's not looking to become a conglomerate."

The analyst added: "But obviously, anything's possible."

Wolff notes that the rumor itself has served a purpose.

"The rumors and conjectures about it are good for Apple and Twitter," Wolff told CNBC.com. "It's not all that likely, but the conjecture is useful for both companies."

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