We investigate the spin-1/2 Heisenberg model on a rectangular lattice, using the Gutzwiller projected variational wave function known as the staggered flux state. Using Monte Carlo techniques, the variational parameters and instantaneous spin-spin correlation function for different coupling anisotropies gamma = J(y)/J(x) are calculated. We observe a gradual evolution of the ground state energy towards a value which is very close to the one-dimensional (1D) estimate provided by the Bethe ansatz and a good agreement between the finite-size scaling of the energies. The spin-spin correlation functions exhibit a power-law decay with varying exponents for different anisotropies. Though the lack of Ned order makes the staggered flux state energetically unfavorable in the symmetric case gamma = 1, it appears to capture the essence of the system close to 1D. Hence we believe that the staggered flux state provides an interesting starting point to explore the crossover from quantum disordered chains to the Neel ordered two-dimensional square lattices.