Normal states of the attractive Hubbard model, mainly in two dimensions, are studied in the context of a transition from a Fermi liquid to an insulating or gapped state. A series of variational Monte Carlo calculations with better statistics was carried out to estimate accurately the expectation values of several many-body wave functions. Although a relatively clear crossover is observed, even for the plain Gutzwiller wave function, the states in both regimes are metallic. Meanwhile, a substantial metal-insulator transition takes place at |U| ∼ W (band width) for an improved wave function, into which an intersite correlation is introduced by taking account of virtual states in the second-order perturbation in the infinite |U| limit. The critical value compares favourably with recent results of the dynamical-mean-field approximation. In contrast, a conventional Jastrow-type wave function scarcely improves the normal state. In addition, the issue of the Brinkman-Rice metal-insulator transition is reconsidered with much larger systems.