Despite being the world’s most valuable company and making, arguably, the coolest and most desirable tech products on the planet, Apple’s been decidedly amateur when it comes to social media. iTunes aside, Apple doesn’t really do much on the major social platforms, and their attempt at building a network of their own, Ping, was a massive flop.

Apple’s always had a special relationship with Twitter, however, which makes this rumour that the Cupertino firm was – and perhaps still is – interested in buying a stake in our favourite micro-blogging network all the more juicy.

The story, which originated in The New York Times yesterday and has been widely circulated, reports that Apple had been considering an investment in the “hundreds of millions of dollars” which, if successful, would value Twitter at more than $10 billion, well above the $8 billion pricing the company received last year. And even an investment of half a billion or more would be peanuts for Apple, which has $117 billion of liquid investments and an absolute boatload of disposable cash.

Investment aside, Twitter, of course, has already secured an important role as a key part of Apple’s future, as the platform has been deeply integrated into Mountain Lion, the latest update to the Apple desktop operating system.

And Twitter loves Apple. “Those guys are a great partner,” said Twitter CEO Dick Costole of Apple recently. “We think of them as a company that our company looks up to.”

The problem? Twitter doesn’t need the money. In fact, they have “truckloads of money in the bank”, says Costolo, which, thanks to some savvy financing and income from their ad platform, analysts project could be upwards of $600 million. Sure, that’s a long way from Apple’s cashpile, but it’s more than enough to remain independent.

For now, at least. Twitter still isn’t profitable, and the company is yet to show a business plan or demonstrate a revenue model that will change that. An investment from Apple would almost guarantee them a future, and also provide Apple with one of the few nuts that they’ve been unable to crack – a proven social platform that has serious legs.

Until then, it’s important to remember that this is just a rumour (and some reports say an old one, at that), that comes with the usual (annoyingly) anonymous sources. We’ll update this story if and when we hear more.