In this paper, we present a proof-ofconcept of a coreference-aware decoder for document-level machine translation. We consider that better translations should have coreference links that are closer to those in the source text, and implement this criterion in two ways. First, we define a similarity measure between source and target coreference structures, by projecting the target ones onto the source ones, and then reusing existing monolingual coreference metrics. Based on this similarity measure, we re-rank the translation hypotheses of a baseline MT system for each sentence. Alternatively, to address the lack of diversity of mentions among the MT hypotheses, we focus on mention pairs and integrate their coreference scores with MT ones, resulting in post-editing decisions. Experiments with Spanish-to-English MT on the AnCora-ES corpus show that our second approach yields a substantial increase in the accuracy of pronoun translation, while BLEU scores remain constant.