This paper identifies some of the main challenges of data governance modelling in the context of learning analytics for higher education institutions, and discusses the critical factors for designing data governance models for learning analytics. It identifies three fundamental common challenges that cut across any learning analytics data governance model, viz., the ownership of the learning analytics data sets, the interpretation of the data, and the decision making based on the data. It also proposes a set of high-level requirements necessary for modelling data governance for learning analytics.