As a prospective study for a future exploration of Venus, we compute the tidal response of Venus' interior assuming various mantle compositions and temperature profiles representative of different scenarios of Venus' formation and evolution. The mantle density and seismic velocities are modeled from thermodynamical equilibria of mantle minerals and used to predict the moment of inertia, Love numbers, and tide-induced phase lag characterizing the signature of the internal structure in the gravity field. The viscoelasticity of the mantle is parameterized using an Andrade rheology. From the models considered here, the moment of inertia lies in the range of 0.327 to 0.342, corresponding to a core radius of 2900 to 3450 km. Viscoelasticity of the mantle strongly increases the potential Love number relative to previously published elastic models. Due to the anelasticity effects, we show that the possibility of a completely solid metal core inside Venus cannot be ruled out based on the available estimate of k2 from the Magellan mission (Konopliv and Yoder, 1996). A Love number k2 lower than 0.27 would indicate the presence of a fully solid iron core, while for larger values, solutions with an entirely or partially liquid core are possible. Precise determination of the Love numbers, k2 and h2, together with an estimate of the tidal phase lag, are required to determine the state and size of the core, as well as the composition and viscosity of the mantle.