Influenza A virus (IAV) has a segmented genome, which (i) allows for exchange of gene segments in coinfected cells, termed reassortment, and (ii) necessitates a selective packaging mechanism to ensure incorporation of a complete set of segments into virus particles. Packaging signals serve as segment identifiers and enable segment-specific packaging. We have previously shown that packaging signals limit reassortment between heterologous IAV strains in a segment-dependent manner. Here, we evaluated the extent to which packaging signals prevent reassortment events that would raise concern for pandemic emergence. Specifically, we tested the compatibility of hemagglutinin (HA) packaging signals from H5N8 and H7N9 avian IAVs with a human seasonal H3N2 IAV. By evaluating reassortment outcomes, we demonstrate that HA segments carrying H5 or H7 packaging signals are significantly disfavored for incorporation into a human H3N2 virus in both cell culture and a guinea pig model. However, incorporation of the heterologous HAs was not excluded fully, and variants with heterologous HA packaging signals were detected at low levels in vivo, including in na?ve contact animals. This work indicates that the likelihood of reassortment between human seasonal IAV and avian IAV is reduced by divergence in the RNA packaging signals of the HA segment. These findings offer important insight into the molecular mechanisms governing IAV emergence and inform efforts to estimate the risks posed by H7N9 and H5N8 subtype avian IAVs.