The current management of the bigeye tuna (Thunnus obesus) fishery in the Western and Central Pacific Ocean (WCPO) is based on a “single-stock” paradigm. We investigated the spatial and temporal distribution of the neutral and potentially adaptive genetic diversity in samples collected from waters near Micronesia, Marshall, Phoenix and Gilbert Islands and French Polynesia using genotyping by sequence and single nucleotide polymorphisms (SNP). Analysis of 144 individuals and 2,682 SNP did not provide any substantial evidence to challenge the current assumption of panmixia in the WCPO using putatively neutral loci. However, there was a signal of potentially adaptive divergence (FST range 0.11–0.24) of samples collected in 2013 in the exclusive economic zone of the Phoenix Islands, possibly because of exposure to differing selective constraints. The geographic origin of these tuna remains to be determined, as the samples originate from tagging cruises that sample large schools of tuna, and some of those tuna have subsequently showed substantial movement. We highly recommend further studies involving large sample sizes of larvae and young-of-the-year across the region and over multiple years to uncover the underlying processes that are potentially driving adaptive divergence and to infer any biological significance it may have on conservation and management of tropical bigeye tuna fishery stock.