Efficiently computing spatio-textual queries has become increasingly important in various applications that need to quickly retrieve geolocated entities associated with textual information, such as in location-based services and social networks. To accelerate such queries, several works have proposed combining spatial and textual indices into hybrid index structures. Recently, the novel idea of replacing traditional indices with ML models has attracted a lot of attention. This includes works on learned spatial indices, where the main challenge is to address the lack of a total ordering among objects in a multidimensional space. In this work, we investigate how to extend this novel type of index design to the case of spatio-textual data. We study different design choices, based on either loose or tight coupling between the spatial and textual part, as well as a hybrid index that combines a traditional and a learned component. We also perform an experimental evaluation using several real-world datasets to assess the potential benefits of using a learned index for evaluating spatio-textual queries.