Federated learning techniques aim to train and build machine learning models based on distributed datasets across multiple devices while avoiding data leakage. The main idea is to perform training on remote devices or isolated data centers without transferring data to centralized repositories, thus mitigating privacy risks. Data analytics in education, in particular learning analytics, is a promising scenario to apply this approach to address the legal and ethical issues related to processing sensitive data. Indeed, given the nature of the data to be studied (personal data, educational outcomes, and data concerning minors), it is essential to ensure that the conduct of these studies and the publication of the results provide the necessary guarantees to protect the privacy of the individuals involved and the protection of their data. In addition, the application of quantitative techniques based on the exploitation of data on the use of educational platforms, student performance, use of devices, etc., can account for educational problems such as the determination of user profiles, personalized learning trajectories, or early dropout indicators and alerts, among others. This paper presents the application of federated learning techniques to a well-known learning analytics problem: student dropout prediction. The experiments allow us to conclude that the proposed solutions achieve comparable results from the performance point of view with the centralized versions, avoiding the concentration of all the data in a single place for training the models.