Device-to-device (D2D) communication not only expected to leverage the energy efficiency in the devices side but also on the network side. The previous works usually only address the energy efficiency of device discovery, which is an important process in D2D, in device side. In this work, we addressed the energy-efficiency of a network element during D2D device discovery. First, we adapted energy calculation for base station energy efficiency in independent device discovery. Second, we also adapted energy calculation for base station energy efficiency in network-assisted device discovery. Third, we conducted simulation to examine base station energy efficiency in both cases. Our simulation result shows that base station energy efficiency can be maximized by utilizing independent device discovery with multiple CHs in a cluster.