According to an article published by MCV, Microsoft has notifying partners that the upcoming Xbox console will not include a disc drive. The source for MCV has described the announcement having "the strictest NDA" they have ever witnessed - but it clearly wasn't that strict.
It has been said that the replacement for the disc drive will be a solid state card. This would then make the Xbox 720, as some believe it will be called, a digital-based console.
Microsoft has responded to this report saying that the "Xbox 360 has found new ways to extend its lifecycle like introducing the world to controller-free experiences with Kinect and re-inventing the console with a new dashboard and new entertainment content partnerships."
"We are always thinking about what is next for our platform and how to continue to defy the lifecycle convention. Beyond that we do not comment on rumors or speculation."
This lends credence to the claims, although it's unclear if Microsoft would be willing to embrace a purely digital model. Sony has stated in the past that it wouldn't be able to do so, because so many countries don't have good enough internet to support the technology.