Instead, says AppleInsider's sources, it'll use "something described as an 'SSD Card'" for storage that's more like a stick of RAM than a traditional hard drive, a proprietary SSD alternative designed by Apple. It's almost like an SSD that's shed the bulk of a hard drive enclosure (since SSDs are basically just bundles of memory chips inside of a hard drive casing), but integrated, so it'll take up less room in the notebook.
It makes a lot sense, actually, to dump a hard drive enclosure's weight and bulk, particularly in a machine that's supposedly only 11.6 inches (and presumably even lighter than the original Air). It's a lot like when Apple ditched replaceable batteries in the MacBook Pros. Using only flash storage would also mean that the Air would be instant on, and more like an iPad in that regard.