According to the New York Times, Apple executives had been in talks with the folks from Twitter recently about making an investment that could take the value of the social media company from it’s $8.4 billion worth last year to over $10 billion.  From the report:

While Apple has been hugely successful in selling phones and tablets, it has little traction in social networking, which has become a major engine of activity on the Web and on mobile devices. Social media are increasingly influencing how people spend their time and money — an important consideration for Apple, which also sells applications, games, music and movies.

Neither company has responded to the rumors, but this would be another huge feather in Apple’s cap.