U.S. technology firms Apple and Twitter are both keeping close-mouthed about the chance of a strategic investment by Apple into the popular social Web site. While both companies said they would not comment on rumors, people close to the companies said there has been talk between the two concerning an expansion of their already beneficial relationship, The New York Times reported Saturday. Comments from the head offices of each firm tell a bit of the story. \"We think of them as a company that our company looks up to,\" said Twitter Chief Executive Officer Dick Costolo recently. \"Those guys are a great partner,\" he said. Tim Cook, CEO at Apple said: \"Apple doesn\'t have to own a social network. But does Apple need to be social? Yes.\" The Times reported that several of Apple\'s new devises are already customized to fit Twitter\'s technical parameters. The problem, however, is that Apple has a ton of cash -- $117 billion in liquid assets -- but Twitter has \"a truckloads of money in the bank,\" Costolo said recently. Apple, nonetheless, could invest hundreds of millions in Twitter, which would push the value of the company from about $8 billion to about $10 billion. Twitter has something almost any company wants out of an online firm: 140 million monthly visitors. Apple\'s relationship with Facebook, meanwhile, has been problematic given Apple\'s Web site Ping failed in an attempt to incorporate some Facebook features, the Times said.