We evolve models of rotating massive stars up to the stage of iron core collapse using the mesa code and find a shell with a mixed composition of primarily helium and oxygen in some cases . In the parameter space of initial masses of 13 - 40 M _ { \odot } and initial rotation velocities of 0 - 450 ~ { } \mathrm { km } ~ { } \mathrm { s } ^ { -1 } that we investigate , we find a mixed helium-oxygen ( He-O ) shell with a significant total He-O mass and with a helium to oxygen mass ratio in the range of 0.5 - 2 only for a small fraction of the models . While the shell formation due to mixing is instigated by rotation , the pre-collapse rotation rate is not very high.The fraction of models with a shell of He-O composition required for an energetic collapse-induced thermonuclear explosion is small , as is the fraction of models with high specific angular momentum , which can aid the thermonuclear explosion by retarding the collapse . Our results suggest that the collapse-induced thermonuclear explosion mechanism that was revisited recently can account for at most a small fraction of core-collapse supernovae . The presence of such a mixed He-O shell still might have some implications for core-collapse supernovae , such as some nucleosynthesis processes when jets are present , or might result in peculiar sub-luminous core-collapse supernovae . Key words : stars : massive — stars : rotation — supernovae : general