  Both the broad iron (Fe) line and the frequency of the kilohertz
quasi-periodic oscillations (kHz QPOs) in neutron star low-mass X-ray binaries
(LMXBs) can potentially provide independent measures of the inner radius of the
accretion disc. We use XMM-Newton and simultaneous Rossi X-ray Timing Explorer
observations of the LMXB 4U 1636-53 to test this hypothesis. We study the
properties of the Fe-K emission line as a function of the spectral state of the
source and the frequency of the kHz QPOs. We find that the inner radius of the
accretion disc deduced from the frequency of the upper kHz QPO varies as a
function of the position of the source in the colour-colour diagram, in
accordance with previous work and with the standard scenario of accretion disc
geometry. On the contrary, the inner disc radius deduced from the profile of
the Fe line is not correlated with the spectral state of the source. The values
of the inner radius inferred from kHz QPOs and Fe lines, in four observations,
do not lead to a consistent value of the neutron star mass, regardless of the
model used to fit the Fe line. Our results suggest that either the kHz QPO or
the standard relativistic Fe line interpretation does not apply for this
system. Furthermore, the simultaneous detection of kHz QPOs and broad Fe lines
is difficult to reconcile with models in which the broadening of the Fe line is
due to the reprocessing of photons in an outflowing wind.
