Participatory budgeting is a democratic innovation that allows citizens to propose and vote on public investment projects. To help organizers manage large volumes of submissions, we design and test privacy-preserving methods for algorithmic shortlisting. These algorithms predict which projects are likely to be funded using only project features and anonymous historical voting data. We demonstrate the limitations of a naive approach that uses a large language model to rank projects based on past success and propose a vote-based pipeline that enables state-of-the-art LLMs to perform on par with classical machine learning. Our findings indicate that user preferences in participatory budgeting are stable enough to allow algorithmic shortlisting to approximate an initial selection of projects effectively.