The New York Times is reporting that Apple might invest some of its considerable cash reserves in Twitter. After the unrewarded experiment that was Ping, Apple put a few hundred million dollars in Twitter in return for tighter cooperation between the companies and sharing Twitter's insight into the social media world. The conversations over the past few months have been private, the NYT reports, and the two companies are not in active negotiations right now. If there were to be an investment, however, it could raise Twitter's value to more than $10 billion.