We present infrared interferometric observations of the inner regions of two A-star debris disks, beta Leo and direct sum Lep, using the FLUOR instrument at the CHARA interferometer on both short (30 m) and long (> 200 m) baselines. For the target stars, the short-baseline visibilities are lower than expected for the stellar photosphere alone, while those of a check star, delta Leo, are not. We interpret this visibility offset of a few percent as a near-infrared (NIR) excess arising from dust grains which, due to the instrumental field of view, must be located within several AU of the central star. For beta Leo, the NIR excess-producing grains are spatially distinct from the dust which produces the previously known mid-infrared (MIR) excess. For direct sum Lep, the NIR excess may be spatially associated with the MIR excess-producing material. We present simple geometric models which are consistent with the NIR and MIR excesses and show that for both objects, the NIR-producing material is most consistent with a thin ring of dust near the sublimation radius, with typical grain sizes smaller than the nominal radiation pressure blowout radius. Finally, we discuss possible origins of the NIR-emitting dust in the context of debris disk evolution models.