Relational mapping, a cognitive sub-process of relational reasoning, plays a critical role in identifying similarities between abstract constructs. This paper discusses an initial endeavor in developing a biologically-inspired spiking neuron model that performs relational mapping in a similar functional manner to existing cognitive models founded in neuroscience. Using spiking neurons provides a capability to portray neural dynamics that naturally lead to notions of critical relational mapping sub-functions such as binding by synchrony. The model, although still in progress, is a step in the direction of progressing cognitive concepts down to an individual spiking neuron level.