The two companies are engaging in discussions, but a deal isn't imminent, according to Bloomberg, which spoke with ESPN executive Sean Bratches. If a deal were to be struck ESPN subscribers would be able to watch ESPN's streaming content via the Apple TV.
WatchESPN is already available on the go with the iPad and iPhone, though it requires customers to subscribe to a participating cable operator. WatchESPN can also be accessed on Microsoft's Xbox 360 gaming console.
Disney frequently works closely with Apple, as Steve Jobs was the largest shareholder of the company after he sold Pixar, and Disney CEO Bob Iger became a member of Apple's board of directors last November.
"We're a platform-agnostic company," Bratches said. "To the extent that in the future there's an opportunity with Apple to authenticate through the pay-TV food chain as we're doing with Microsoft, that's something we'll participate in."
In March, it was said that ESPN was working with Apple on potentially bringing live sports scores to the Siri voice assistant application on the iPhone 4S. ESPN and ABC Sports were also the first to offer sports programming on Apple's iTunes in 2006.
The Apple TV already offers a number of streaming content options, including a number of sports-centric services like NHL Gamecenter, MLB.tv and NBA League Pass.