Aqueous suspensions of Laponite, a system composed of disklike nanopartides, are found to develop optical birefringence over several days, well after the suspensions solidified because of jamming. The optical anisotropy is particularly enhanced near the air-Laponite suspension interface over length scales of several millimeters, which is beyond 5 orders of magnitude larger than the particle length scale, suggestive of large-scale ordering influenced by the interface. The orientational order increases with time and is always greater for higher concentration of salt, higher concentration of Laponite, and higher temperatures of the suspension. Although weakly birefringent, Laponite suspensions covered by paraffin oil do not show any enhancement in optical anisotropy near the interface compared to that in the bulk. We suggest that the expedited structure formation near the air interface propagating progressively inside the sample is responsible for the observed behavior. We discuss the observed nematic ordering in the context of glass-like and gel-like microstructure associated with aqueous Laponite suspensions.