Data spaces consist of trusted frameworks that manage the entire data lifecycle, encompassing various data models, metadata descriptors, ontologies for semantic interpretation, and data services for accessing, processing, and analyzing data. Domain-specific data spaces are currently being designed and deployed in vertical sectors, following specifications and reference frameworks that enable interoperability and compatibility. One such vertical sector with high impact on economy is mobility. In this paper, we present our position towards mobility data spaces, highlighting the idiosyncrasy of mobility data, while presenting the MobiSpaces approach that encompasses services for mobility data management and advanced mobility analytics. By exploiting MobiSpaces, mobility data providers can break the barrier of participation in data spaces thereby sharing their dataset with less hurdle, whereas data consumers can find advanced data analysis tools readily applicable on mobility data sets to extract insights and discover mobility patterns.