Planning methods often struggle with computational intractability when solving task-level problems in large-scale environments. This work explores how the commonsense knowledge encoded in Large Language Models (LLMs) can be leveraged to enhance planning techniques for such complex scenarios. Specifically, we propose an approach that uses LLMs to efficiently prune irrelevant components from the planning problem's state space, thereby substantially reducing its complexity. We demonstrate the efficacy of our system through extensive experiments in a household simulation environment as well as real-world validation on a 7-DoF manipulator (video: https://youtu.be/6ro2UOtOQS4).