A search for the $\phi$-meson bound state itself is already quite interesting, although it seems to be natural that the $\phi$ forms a stable nuclear bound state. Compared to other vector-meson studies, the $\phi$ is quite interesting due to its narrow width. Since the $\phi$ barely interacts with surrounding nucleons, it is natural to have a narrow width even in nuclei. In fact, the width broadening in nuclear media is reported to be only 3.4 times that of free space. This fact makes the discrete peak observation in the missing mass feasible and allows simple analysis of the mass shift from the systematic study of the binding energies over several nuclei. A systematic study over several nuclear targets will yield a unique, definitive and precise determination of the in-medium mass modification of the vector meson $\phi(s\overline{s})$. Recently, we proposed new idea of the experiment to study in-medium mass modification of the $\phi$ meson via the formation of $\phi$ meson bound state to J-PARC. In this presentation, we will demonstrate that a completely background-free missing-mass spectrum can be obtained efficiently by $(\overline{p}, \phi)$ spectroscopy together with the $K^+\Lambda$ tagging, using the primary reaction channel $\overline{p} p \rightarrow \phi \phi$. From both missing mass and invariant mass study of the sub-threshold energy region, one can independently deduce the mass shift information.