Human motion prediction is an essential component for enabling closer human-robot collaboration. The task of accurately predicting human motion is non-trivial. It is compounded by the variability of human motion, both at a skeletal level due to the varying size of humans and at a motion level due to individual movement's idiosyncrasies. These variables make it challenging for learning algorithms to obtain a general representation that is robust to the diverse spatio-temporal patterns of human motion. In this work, we propose a modular sequence learning approach that allows end-to-end training while also having the flexibility of being fine-tuned. Our approach relies on the diversity of training samples to first learn a robust representation, which can then be fine-tuned in a continual learning setup to predict the motion of new subjects. We evaluated the proposed approach by comparing its performance against state-of-the-art baselines. The results suggest that our approach outperforms other methods over all the evaluated temporal horizons, using a small amount of data for fine-tuning. The improved performance of our approach opens up the possibility of using continual learning for personalized and reliable motion prediction.