TiVo-powered Apple TV? Don't hold your breath
For starters, while TiVo is still one of the prettiest and most intuitive ways to access DVR content, Apple's more likely to copy the best features rather than partner with a company that just switched over to a Flash-based user interface and already has partnerships with many rivals.
Next, TiVo is well-known for organizing content you record from your local cable or satellite provider, a task that it has had trouble competing in lately, rather than organizing loads of digital content purchased online from a store like iTunes or from a local collection.
If the more detailed rumors of what Apple's next generation Apple TV will look like are to be believed, it won't be a device you hook up to cable, but instead will be a cloud-based media hub that connects and entertains on a more a la carte model of distributing TV than your local cable company will be able to provide.
With any luck the next Apple TV will be something to shake up a market that is built around a few powerful companies and a distribution model that thrives on a lack of choices.