The mass and decay width of the $\phi$ meson in cold nuclear matter are computed in an effective Lagrangian approach, with the medium
dependence of these properties obtained by evaluating
kaon-antikaon loop contributions to the $\phi$ self-energy.
At normal nuclear matter density, we find a downward shift of the $\phi$ mass by a few percent, while the decay width is enhanced by an order of magnitude. We also present $\phi$--nucleus bound state energies and absorption widths for some selected nuclei, using complex optical potentials obtained in the local density approximation. Our results suggest that the $\phi$ should form
bound states with all the nuclei considered. However, the identification of the signal for these predicted bound states will need careful investigation because of their sizable absorption widths.