We report the search for low-mass X-ray binaries in quiescence (qLMXBs) in the globular cluster NGC 6304 using XMM observations. We present the spectral analysis leading to the identification of three candidate qLMXBs within the field of this globular cluster (GC), each consistent with the X-ray spectral properties of previously identified qLMXBs in the field and in other globular clusters -- specifically, with a hydrogen atmosphere neutron star with radius between 5--20km. One (source 4, with R=11.7^{+8.3}_{-0.4} (D/5.97 kpc) km and kT_eff=117^{+59}_{-44} eV) is located within one core radius (r_c) of the centre of NGC 6304. This candidate also presents a spectral power-law component contributing 49 per cent of the 0.5-10 keV flux. A second one (source 9 with R=15.3^{+11.2}_{-6.5} (D/5.97 kpc) km and kT_eff=100^{+24}_{-19} eV) is found well outside the optical core (at 32 r_c) but still within the tidal radius. From spatial coincidence, we identify a bright 2MASS infrared counterpart which, at the distance of NGC 6304, seems to be a post-asymptotic giant branch star. The third qLMXB (source 5 with R=23^{+38}_{-14} (D/5.97 kpc) km and kT_eff=70^{+28}_{-20} eV) is a low signal-to-noise candidate for which we also identify from spatial coincidence a bright 2MASS infrared counterpart, with 99.916 per cent confidence. Three qLMXBs from this GC is marginally consistent with that expected from the encounter rate of NGC 6304. We also report a low signal-to-noise source with an unusually hard photon index (alpha=-2.0^{+1.2}_{-2.2}). Finally, we present an updated catalogue of the X-ray sources lying in the field of NGC 6304, and compare this with the previous catalogue compiled from ROSAT observations.
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