The formation of η-meson-nucleus bound states is investigated, using a standard Green's function method of many-body problems. Within physically reasonable range of the parameters (coupling constants and harmonic oscillator potentials), we find that the η- 16O bound state is indeed possible and depends crucially on the channel ( N ∗← Nη) being attractive, where N ∗ is the πN resonance with (I, J p) = ( 1 2 , 1 2 −) and mass m = 1535 MeV. Our results indicate that the wavefunction of this state is mainly of the N ∗-particle-N-hole structure. Experimental studies of η-nucleus bound states are suggested.