The aim of this work is to study the capabilities of the Futur Circular Collider (FCC) $ee$ phase to study the transitions $b\to s\tau^+\tau^-$ unobserved to date. At meson scale the decay $B^0\to K^*\tau^+\tau^-$ with the transition $\tau\to\pi\pi\pi\nu_{\tau}$ is studied with a method to reconstruct explicitly the two undetected neutrinos. The detector requirements to study this decay are evaluated, in particular the vertexing resolution performance. Some conclusions about the main drivers of the detector performance are drawn by means of the analysis of signal simulated sample. Finally, simulated samples of the most toxic backgrounds (coming from $b\to c\bar{c}s$ and $b\to c\tau\nu$) are injected in the system and allow the exploration of the feasibility of $b\to s\tau^+\tau^-$ measurement at FCC $ee$.