Noble gas isotopes in plumes require a source of primitive volatiles largely isolated in the Earth for 4.5 Gyrs. Among the proposed reservoirs, the core is gaining interest in the absence of robust geochemical and geophysical evidence for a mantle source. This is supported by partitioning data showing that sufficient He and Ne could have been incorporated into the core to source plumes today. Here we perform ab initio calculations on the partitioning of He, Ne, Ar, Kr and Xe between liquid iron and silicate melt under core forming conditions. For He our results are consistent with previous studies allowing for substantial amounts of He in the core. In contrast, the partition coefficient for Ne is three orders of magnitude lower than He. This very low partition coefficient would result in a 3He/22Ne ratio of ~103 in the core, far higher than observed in ocean island basalts (OIBs). We conclude that the core is not the source of noble gases in OIBs.