Fin whales (Balaenoptera physalus) and blue whales (B. musculus) are the two largest species on Earth and are widely distributed across the world's oceans. Hybrids between these species appear to be relatively widespread and have been reported in both the North Atlantic and North Pacific; they are also relatively common, and have been proposed to occur once in every thousand fin whales. However, despite known hybridization, fin and blue whales are not sibling species. Rather, the closest living relative of fin whales are humpback whales (Megaptera novaeangliae). To improve the quality of fin whale data available for analysis, we assembled and annotated a fin whale nuclear genome using in-silico mate pair libraries and previously published short-read data. Using this assembly and genomic data from a humpback, blue, and bowhead whale, we investigated whether signatures of introgression between the fin and blue whale could be found. We find no signatures of contemporary admixture in the fin and blue whale genomes, although our analyses support ancestral gene flow between the species until 2.4-1.3 Ma. We propose the following explanations for our findings; i) fin/blue whale hybridization does not occur in the populations our samples originate from, ii) contemporary hybrids are a recent phenomenon and the genetic consequences have yet to become widespread across populations, or iii) fin/blue whale hybrids are under large negative selection, preventing them from backcrossing and contributing to the parental gene pools.