This paper presents the EACare project, an ambitious multi-disciplinary collaboration with the aim to develop an embodied system, capable of carrying out neuropsychological tests to detect early signs of dementia, e.g., due to Alzheimer's disease. The system will use methods from Machine Learning and Social Robotics, and be trained with examples of recorded clinician-patient interactions. The interaction will be developed using a participatory design approach. We describe the scope and method of the project, and report on a first Wizard of Oz prototype.