Concepts, both abstract and concrete, elicit a distribution of association strengths across perceptual color space, which influence aspects of visual cognition ranging from object recognition to interpretation of information visualizations. While prior work has hypothesized that color-concept associations may be learned from the cross-modal statistical structure of experience, it has been unclear whether natural environments possess such structure or, if so, whether learning systems are capable of discovering and exploiting it without strong prior constraints. We addressed these questions by investigating the ability of GPT-4, a multimodal large language model, to estimate human-like color-concept associations without any additional training. Starting with human color-concept association ratings for 71 color set spanning perceptual color space (\texttt{UW-71}) and concepts that varied in abstractness, we assessed how well association ratings generated by GPT-4 could predict human ratings. GPT-4 ratings were correlated with human ratings, with performance comparable to state-of-the-art methods for automatically estimating color-concept associations from images. Variability in GPT-4's performance across concepts could be explained by specificity of the concept's color-concept association distribution. This study suggests that high-order covariances between language and perception, as expressed in the natural environment of the internet, contain sufficient information to support learning of human-like color-concept associations, and provides an existence proof that a learning system can encode such associations without initial constraints. The work further shows that GPT-4 can be used to efficiently estimate distributions of color associations for a broad range of concepts, potentially serving as a critical tool for designing effective and intuitive information visualizations.