This would make a lot of sense in a lot of ways. According to the Verge, the next Xbox will control your TV, and makes some actual sense out of the rumoured "always online" feature of the new console, and some new Kinect features as well.
The functionality will work by taking a cable box signal and passing it through to the Xbox via HDMI, allowing Microsoft's console to overlay a UI and features on top of an existing TV channel or set-top box. We're told that this is a key part of the next-generation Xbox and that it will go a step further than Google's TV implementation thanks to Microsoft's partnerships with content providers.
The Wii U has a similar functionality to this with its TVii feature, though that is through a limited number of providers. The Wii U uses the 5-inch touchscreen on its gamepad to operate as a remote, while the Xbox would presumably use its own standard controller, possible remote control peripherals, and the Kinect.
The Verge says that the Kinect plays a big part in the the living room arrangement. It will apparently be able to detect multiple people at once, and similar to the Samsung Galaxy S4, have the ability to pause when you or anyone looks away from the TV. This seems like a natural pairing, since the main way a lot of people use their Kinect is to control Netflix or HBO Go when their Xbox controller is out of sight.
Microsoft's also been rumoured to be working on a low-cost set-top box for Xbox TV, but word is that it won't be out until next year, while the new Xbox is expected some time this autumn. [Verge]