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 Kα 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 iron line is not correlated with the spectral state of the source. The values of the inner radius inferred from kHz QPOs and iron lines, in four observations, do not lead to a consistent value of the neutron star mass, regardless of the model used to fit the iron 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 iron lines is difficult to reconcile with models in which the broadening of the iron line is due to the reprocessing of photons in an outflowing wind.