The concept of harmonic influence has been recently proposed as a metric for the importance of nodes in a social network. A distributed message passing algorithm for its computation has been proposed by Vassio et al. (2014) and proved to converge on general graphs by Rossi and Frasca (2016a). In this paper, we want to evaluate the convergence time of this algorithm by using a mean-field approach. The mean-field dynamics is first introduced in a “homogeneous” setting, where it is exact, then heuristically extended to a non-homogeneous setting. The rigorous analysis of the mean-field dynamics is complemented by numerical examples and simulations that demonstrate the validity of the approach.