We present the results of a new analysis of the literature data on electron mobility μ in dense helium gas aimed at determining the existence of a threshold density for electron self-trapping in gaseous helium as a function of temperature. We have investigated the density dependence of μ and, when available, its dependence on the electric field. The experimental data are favorably rationalized by minimizing the excess free energy of the self-localized states within the optimum fluctuation model. It is shown that the formation of electron bubbles via the self-trapping phenomenon is determined by the delicate balance between the electron thermal energy, the density dependence of the electron energy at the bottom of the conduction band in the gas, and the work necessary to expand the bubble. We show that the self-trapping phenomenon is not limited to low temperatures but occurs at any temperatures for large enough densities.