The dynamics of the vortex core are investigated in a swirling jet at swirl numbers in the range of the critical swirl number for vortex breakdown. Vortex breakdown, a bifurcation in the structure of a swirling jet, results in the establishment of a stagnation point and recirculation region along the centerline of the jet. In this study, we explore the dynamics of the swirling jet near vortex breakdown. Investigation of time-averaged velocity fields and profiles leads to the identification of three flow regimes: pre-breakdown, near-breakdown, and post-breakdown. Velocity fields in these regimes are further analyzed using dynamic mode decomposition, Rankine-vortex fitting, and proper orthogonal decomposition to characterize jet dynamics with a particular focus on the development of the recirculation region characteristic of vortex breakdown. A precessing vortex core is also identified in the post-breakdown regime and its behavior is discussed.