Consider a bounded Hankel operator Gamma with s-numbers s(0) greater than or equal to s(1) greater than or equal to ... and a sequence of bounded Hankel operators Gamma(n) converging to Gamma in the operator norm. In this paper, it is shown that for each k with s(k-1) > s(k) greater than or equal to s(k+1) greater than or equal to ..., the rational symbols of the best rank-k Hankel approximants of Gamma(n) converge uniformly to the corresponding rational symbol of the best rank-k Hankel approximant of Gamma. Based on this continuity result, the convergence of the near-best Hankel approximants corresponding to a fairly general class of truncated Hankel operators is discussed.