The thermonuclear reaction rates and Maxwellian-averaged cross-sections (MACS) for the \(^{84}\) Kr(n, \(\gamma\) ) \(^{85}\) Kr and \(^{86}\) Kr(n, \(\gamma\) ) \(^{87}\) Kr processes were examined using the statistical model code Talys v1.96. The effects of nuclear level densities (NLDs) on Maxwellian-averaged cross-sections and neutron capture rates are examined both quantitatively and qualitatively. The present Talys-based MACS and radiative capture rates for \(^{84}\) Kr(n, \(\gamma\) ) \(^{85}\) Kr and \(^{86}\) Kr(n, \(\gamma\) ) \(^{87}\) Kr processes agree well with the earlier reported findings. The statistical model’s nuclear properties (level density and gamma ray strength) were fine-tuned to reproduce the existing experimental nuclear data.