Privacy is a software quality that is closely related to security. The main difference is that security properties aim at the protection of assets that are crucial for the considered system, and privacy aims at the protection of personal data that are processed by the system. The identification of privacy protection needs in complex systems is a hard and error prone task. Stakeholders whose personal data are processed might be overlooked, or the sensitivity and the need of protection of the personal data might be underestimated. The later personal data and the needs to protect them are identified during the development process, the more expensive it is to fix these issues, because the needed changes of the system-to-be often affect many functionalities. In this paper, we present a systematic method to identify the privacy needs of a software system based on a set of functional requirements by extending the problem-based privacy analysis (ProPAn) method. Our method is tool-supported and automated where possible to reduce the effort that has to be spent for the privacy analysis, which is especially important when considering complex systems. The contribution of this paper is a semi-automatic method to identify the relevant privacy requirements for a software-to-be based on its functional requirements. The considered privacy requirements address all dimensions of privacy that are relevant for software development. As our method is solely based on the functional requirements of the system to be, we enable users of our method to identify the privacy protection needs that have to be addressed by the software-to-be at an early stage of the development. As initial evaluation of our method, we show its applicability on a small electronic health system scenario.