  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--20\km. 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.
