We are interested in finding clusters of time series such that series within a cluster are correlated and series between clusters are independent. Existing Bayesian methods for inferring correlated clusters of time series either: (i) require conditioning on latent variables to decouple time series, but results in slow mixing or (ii) require calculating a collapsed likelihood, but with computation scaling cubically with the number of time series per cluster. To infer the latent cluster assignments efficiently, we consider approximate methods that trade exactness for scalability. Our main contribution is the development of an expectation propagation based approximation for the collapsed likelihood approach. Our empirical results on synthetic data show our methods scale linearly instead of cubically, while maintaining competitive accuracy.