Conventional retrieval-augmented neural machine translation (RANMT) systems leverage bilingual corpora, e.g., translation memories (TMs). Yet, in many settings, monolingual corpora in the target language are often available. This work explores ways to take advantage of such resources by directly retrieving relevant target language segments, based on a source-side query. For this, we design improved cross-lingual retrieval systems, trained with both sentence level and word-level matching objectives. In our experiments with three RANMT architectures, we assess such cross-lingual objectives in a controlled setting, reaching performances that match those of standard TM-based models. We also showcase our method on a real-world settings, using much larger monolingual and observe strong improvements over both the baseline setting and general-purpose cross-lingual retrievers.