There is currently debate about the extent to which non-linguistic beings such as human infants and great apes are capable of absent reference. In a series of experiments we investigated the flexibility and specificity of great apes' (N=36) and 12 month-old infants' (N=40) requests for absent entities. Subjects had the choice between requesting visible objects directly and using the former location of a depleted option to request more of these now-absent entities. Importantly, we systematically varied the quality of the present and absent options. We found that great apes as well as human infants flexibly adjusted their requests for absent entities to these contextual variations and only requested absent entities when the visible option was of lower quality than the absent option. These results suggest that the most basic cognitive capacities for absent reference do not depend on language and are shared by humans and their closest living relatives.