Learning by imitation involves not only perceiving another individual's action to copy it, but also the formation of a memory trace in order to gradually establish a correspondence between the sensory and motor codes, which represent this action through sensorimotor experience. Memory and sensorimotor processes are closely intertwined. Mirror neurons, which fire both when the same action is performed or perceived, have received considerable attention in the context of imitation. An influential view of memory processes considers that the consolidation of newly acquired information or skills involves an active offline reprocessing of memories during sleep within the neuronal networks that were initially used for encoding. Here, we review the recent advances in the field of mirror neurons and offline processes in the songbird. We further propose a theoretical framework that could establish the neurobiological foundations of sensorimotor learning by imitation. We propose that the reactivation of neuronal assemblies during offline periods contributes to the integration of sensory feedback information and the establishment of sensorimotor mirroring activity at the neuronal level.