Humans have a powerful ability to generate novel compositional representations. For example, imagining a pink banana requires compositional mappings between signifiers pink and banana and the perceptual referents of these signifiers. This essential cognitive faculty remains challenging to model in a biologically plausible way. Here, we present a model that implements signifier-referent compositional associations using Hebbian associative learning. The model satisfies the following constraints: (1) once associated, both signific and referential inputs can activate the shared representation, and (2) when signific and referential inputs are compositional, the model should generalize to novel compositional combinations. When trained on MNIST, the model successfully learns to associate number labels with corresponding images. On colored MNIST, the model learns signific-referential associations for both digits and colors, with somewhat successful generalization to new digit-color combinations. This work serves as a proof of concept for biologically plausible models of signifier-referent association.