The online processing of both music and language involves making predictions about upcoming material, but the relationship between prediction in these two domains is not well understood. Electrophysiological methods for studying individual differences in prediction in language processing have opened the door to new questions. Specifically, we ask whether individuals with musical training predict upcoming linguistic material more strongly and/or more accurately than non‐musicians. We propose two reasons why prediction in these two domains might be linked: (a) Musicians may have greater verbal short‐term/working memory; (b) music may specifically reward predictions based on hierarchical structure. We provide suggestions as to how to expand upon recent work on individual differences in language processing to test these hypotheses.