Determining which proteins interact together from their amino acid sequences is an important task. In particular, even if an interaction is known to exist in some species between members of two protein families, determining which other members of these families are interaction partners can be tricky. Indeed, it requires identifying which paralogs interact together. Various methods have been proposed to this end. Here, we present a new one, which relies on a protein language model trained on multiple sequence alignments and directly exploits the fact that this model was trained to fill in masked amino acids. We obtain promising results on two different benchmark pairs of interacting protein families where partners are known. In particular, performance is good even for shallow alignments, while previous coevolution-based methods require deep ones. Performance is also found to quickly improve by giving the model correct examples of interacting sequences.