  We determine the magnetic field dependence of the pseudogap closing
temperature T* within a precursor superconductivity scenario. Detailed
calculations with an anisotropic attractive Hubbard model account for a
recently determined experimental relation in BSCCO between the pseudogap
closing field and the pseudogap temperature at zero field, as well as for the
weak initial dependence of T* at low fields. Our results indicate that the
available experimental data are fully compatible with a superconducting origin
of the pseudogap in cuprate superconductors.
