Time series clustering is a fundamental task in data mining and machine learning with applications spanning healthcare, finance, and industrial systems. However, existing deep clustering methods rely predominantly on recurrent architectures like LSTM and GRU, which struggle with long-term dependencies and computational efficiency. This paper introduces Liquid Time-Constant Networks Clustering (LTC-C), a novel neuromorphic approach that leverages continuous-time neural dynamics with adaptive time constants for temporal clustering. Our method combines a Liquid Time-Constant encoder with a temporal autoencoder framework and employs joint optimization of reconstruction and clustering objectives. Through comprehensive experiments on the UCR Time Series Archive, we demonstrate that LTC-C achieves superior clustering performance compared to traditional Bi-LSTM based approaches across multiple evaluation metrics including Adjusted Rand Index, Normalized Mutual Information, and Area Under Curve. The adaptive temporal dynamics of liquid networks enable our model to capture multi-scale temporal patterns more effectively, making it particularly suitable for complex time series with varying temporal characteristics.