Heat conduction in superlattices demonstrates various atomic-scale effects, one of which is the ultra-low thermal conductivity. Remarkably, theoretical works even promise sub-amorphous thermal conductivity in superlattices made of amorphous materials. Yet, these predictions were not tested experimentally. Here, we experimentally study the cross-plane thermal transport in amorphous Si/SiO2 superlattices at room temperature. Using the micro time-domain thermoreflectance technique, we measured the thermal conductivity of superlattices with periods of 6.6, 11.8, and 25.7 nm. The thermal conductivity values are in the range of 1.1–1.5 W m-1K-1 and generally agree with the values reported for amorphous Si and SiO2. However, the superlattice with the highest density of interfaces seems to have the thermal conductivity slightly below the amorphous limit. These data suggest that heat conduction below the amorphous limit might be possible in amorphous superlattices with a periodicity shorter than 6.6 nm.