The possible existence of (cc¯)-nucleus bound states is examined. We adopt Gaussian potentials for the ηc-N and J/ψ-N interactions. The relations between the scattering lengths a of (cc¯). N interactions and the binding energies of ηc-NN, J/ψ-NN, and J/ψ-4He are given. The results show that scattering lengths a ≤ -0.95 fm are needed to make ηc-NN and J/ψ-NN bound states, while for a ≤ -0.24 fm there may exist a J/ψ-4He bound state.