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A discovery of a permanent electric dipole moment (EDM) of the neutron would provide one of the most important low energy tests of the discrete symmetries beyond the Standard Model of particle physics. A new search of neutron EDM, to be conducted at the spallation neutron source at Oak Ridge National Laboratory, is designed to improve the present experimental limit of ~10-26 e·cm by two orders of magnitude. The experiment is based on the magnetic-resonance technique in which polarized neutrons precess at the Larmor frequency when placed in a static magnetic field; a nonzero EDM would be evident as a difference in precession frequency when a strong external electric field is applied parallel versus antiparallel to the magnetic field. In addition to its role as neutron spin-analyser via the spin-dependent n+3He nuclear capture reaction, polarized helium-3 (which has negligible EDM) will serve as co-magnetometer to correct for drifts in the magnetic field. In one of the two methods that will be built into the apparatus, the helium-3 precession signal is read out by SQUID-based gradiometers. We present a design study of a SQUID system suitable for the neutron EDM apparatus, and discuss using very long leads between the pickup loop and the SQUID.