We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the solution (e.g., a machine learning classifier), one can design simple linear-time algorithms that achieve a $(1-ε)$approximation. Finally, we present experimental results demonstrating the effectiveness of our methods for the densest at-most-$k$ subgraph problem on real-world graphs.