The data market concept has gained a lot of momentum in recent years, fuelled by initiatives to set up such markets, e.g., on the European level. Still, the typical data market concept aims at providing a centralised platform with all of its positive and negative side effects. Internal data markets, also called local or on-premise data markets, on the other hand, are set up to allow data trade inside an institution (e.g., between divisions of a large company) or between members of a small, well-defined consortium, thus allowing the remuneration of providing data inside these structures. Still, while research on securing global data markets has garnered some attention throughout recent years, the internal data markets have been treated as being more or less similar in this respect. In this paper, we outline the major differences between global and internal data markets with respect to security and why further research is required. Furthermore, we provide a fundamental model for a secure internal data market that can be used as a starting point for the generation of concrete internal data market models. Finally, we provide an overview on the research questions we deem most pressing in order to make the internal data market concept work securely, thus allowing for more widespread adoption.