The partition coefficients of potassium, DK, between molten sanidine, KAlSi3O8, and molten roedderite, K2Mg5Si12O30, with FeS-rich alloy and pure Fe metal liquids have been investigated in a multi-anvil press, between 5 and 15 GPa, at a temperature of 2173 K, and at an oxygen fugacity between 0.5 and 3 log units below the iron-wüstite (IW) buffer. No pressure dependence of the DK coefficients in sulphur-free and sulphur-bearing systems was found within the investigated pressure range. We also observed minor effect of the silicate melt composition for an nbo/t (non-bridging oxygen to tetrahedral cation ratio) higher than 0.8 ± 0.4. In contrast, the partitioning of potassium varies strongly with the metallic phase composition, with an increase of K-solubility in the metallic liquid for high sulphur and oxygen contents. We review all available high-pressure data to obtain reliable DK coefficients for the interaction between molten silicates and Fe-alloy liquids at pressures and temperatures relevant to those of core formation in a terrestrial magma ocean. The dominant controlling parameters appear to be the temperature and the chemical composition of the metallic phase, with DK coefficients significantly increased with temperature, and with the sulphur and oxygen contents of the Fe-alloy liquid. Our considerations distinguish two extreme cases, with an S-free or S-bearing iron core, which yield K contents of 25 or 250 ppm, respectively. These two extreme values have very different consequences for thermal budget models of the Earth's core since its formation.