Entity Set Expansion is an important NLP task that aims at expanding a small set of entities into a larger one with items from a large pool of candidates. In this paper, we propose GausSetExpander, an unsupervised approach based on optimal transport techniques. We propose to re-frame the problem as choosing the entity that best completes the seed set. For this, we interpret a set as an elliptical distribution with a centroid which represents the mean and a spread that is represented by the scale parameter. The best entity is the one that increases the spread of the set the least. We demonstrate the validity of our approach by comparing to state-of-the art approaches.