The φ-meson properties in cold nuclear matter are investigated by implementing resonant φN interactions as described in effective approaches including the unitarization of scattering amplitudes. Several N * -like states are dynamically generated in these models around 2 GeV, in the vicinity of the φN threshold. We find that both these states and the non-resonant part of the amplitude contribute sizably to the φ collisional self-energy at finite nuclear density. These contributions are of a similar strength as the widely studied medium effects from theKK cloud. Depending on model details (position of the resonances and strength of the coupling to φN ) we report a φ broadening up to about 40-50 MeV, to be added to the φ →KK in-medium decay width, and an attractive optical potential at threshold up to about 35 MeV at normal matter density. The φ spectral function develops a double peak structure as a consequence of the mixing of resonance-hole modes with the φ quasi-particle peak. The former results point in the direction of making up for missing absorption as reported in φ nuclear production experiments.