It has been proposed that the radio spectra of radio-quiet quasars are produced by free–free emission in the optically thin part of an accretion disc wind. An important observational constraint on this model is the observed X-ray luminosity. We investigate this constraint using a sample of Palomar–Green (PG) radio-quiet quasars for which XMM–Newton European Photon Imaging Camera (EPIC) spectra are available. Comparing the predicted and measured luminosities for 0.5, 2 and 5 keV, we conclude that all of the studied PG quasars require a large hydrogen column density absorber, requiring these quasars to be close to or Compton thick. Such a large column density can be directly excluded for PG 0050+124, for which a high-resolution reflection grating spectrometer spectrum exists. Further constraint on the column density for a further 19 out of the 21 studied PG quasars comes from the EPIC spectrum characteristics such as hard X-ray power-law photon index and the equivalent width of the Fe Kα line; and the small equivalent width of the C iv absorber present in ultraviolet spectra. For two sources, PG 1001+054 and PG 1411+442, we cannot exclude that they are indeed Compton thick, and the radio and X-ray luminosity are due to a wind originating close to the supermassive black hole. We conclude that for 20 out of 22 PG quasars studied, free–free emission from a wind emanating from the accretion disc cannot mutually explain the observed radio and X-ray luminosity.