During language comprehension, listeners often anticipate upcoming information. This can draw listeners’ overt attention to visually presented objects before the objects are referred to. We investigated to what extent the anticipatory mechanisms involved in such language-mediated attention rely on specific verbal factors and on processes shared with other domains of cognition. Participants listened to sentences ending in a highly predictable word (e.g., “In 1969 Neil Armstrong was the first man to set foot on the moon”) while viewing displays containing three unrelated distractor objects and a critical object, which was either the target object (e.g., a moon), or an object with a similar shape (e.g., a tomato), or an unrelated control object (e.g., rice). Language-mediated anticipatory eye movements to targets and shape competitors were observed. Importantly, looks to the shape competitor were systematically related to individual differences in anticipatory attention, as indexed by a spatial cueing task: Participants whose responses were most strongly facilitated by predictive arrow cues also showed the strongest effects of predictive language input on their eye movements. By contrast, looks to the target were related to individual differences in vocabulary size and verbal fluency. The results suggest that verbal and nonverbal factors contribute to different types of language-mediated eye movement. The findings are consistent with multiple-mechanism accounts of predictive language processing.