Wireless signals are a unique form of time-series data that encode rich physical characteristics of the propagation environment. As large volumes of signals are continuously generated in wireless sensing systems, efficient compression is essential for scalable transmission under limited system resources. However, wireless signals exhibit strong variability across environments and time, making it difficult to design universal compression schemes that generalize across domains while preserving the physical fidelity required for accurate reconstruction and sensing. Meanwhile, recent advances in large language models (LLMs) have demonstrated remarkable reasoning and adaptation capabilities across diverse modalities and domains. This raises an intriguing question: can LLMs compress wireless signals in a training-free manner while preserving physical fidelity? To the best of our knowledge, this problem remains unexplored. To answer this question, we propose a physics-informed prompting framework for training-free wireless signal compression. The framework incorporates environmental context and scenario-specific knowledge as physical priors in the prompt. We further introduce a dictionary module with self-learned patterns to stabilize inference and a key prompt module to align the semantics between the LLMs used for compression and reconstruction. Extensive experiments demonstrate that the proposed framework achieves high-fidelity reconstruction under cross-domain settings, highlighting the promise of physics-informed prompting as a new paradigm for processing and compressing low-level physical signals.