Human cerebral organoids (HCOs) are models that grow up in the laboratory and mimic the cellular composition, structure and function of parts of the adult human brain. Recently, an interesting debate has appeared on the ethics of HCO research and application, particularly on the current and future moral status of these entities. A precautionary approach has been proposed, implying a level of protection and moral consideration based on the potential conscious activity that might be detected in future complex forms of HCO. In this article, I aim to broaden the analysis of the question of the moral status of HCOs through an ontological analysis. The hybrid nature of HCOs (between object and subject, natural and artificial) entails an ontological complexity that is difficult to fix in an absolute sense, and this has consequences on the ethical level as well. After identifying the relevant moral concepts at stake, I argue that HCOs can be placed between being moral objects and moral patients based on their ontological status. Therefore, HCOs deserve indirect moral consideration (as moral objects), even if they have not yet or will never develop consciousness; moreover, if they were to reach such a level of complexity that they might have interests in their own self-preservation, they could also receive direct moral consideration (as moral patients). This ontological analysis displays the evolving complexity of these entities, potentially helping define all the factors to be taken into account when formulating the precautionary principle on a case-by-case basis to identify the proper proportionality and regulation of HCOs.