We discuss possible stellar origins of short-lived radioactive nuclei with meanlife τ ≤ 100 Myr, which were shown to be alive in the Early Solar System (ESS). We first review current ideas on the production of nuclides having 10 ≤ τ ≤ 100 Myr, which presumably derive from the continuous interplay of galactic astration, nucleosynthesis from massive supernovae and free decay in the interstellar medium. The abundance of the shorter lived 53Mn might be explained by this same scenario. Then we consider the nuclei 107Pd, 26Al, 41Ca and 60Fe, whose early solar system abundances are too high to have originated in this way. Present evidence favours a stellar origin, particularly for 107Pd, 26Al and 60Fe, rather than an in situ production by energetic solar particles. The idea of an encounter (rather close in time and space) between the forming Sun and a dying star is therefore discussed: this star may or may not have also triggered the solar formation. Recent nucleosynthesis calculations for the yields of the relevant short-lived isotopes and of their stable reference nuclei are discussed. Massive stars evolving to type II supernovae (either leaving a neutron star or a black hole as a remnant) seem incapable of explaining the four most critical ESS radioactivities in their observed abundance ratios. An asymptotic giant branch (AGB) star seems to be a viable source, especially if of relatively low initial mass (M ≤ 3 M⊙) and with low neutron exposure: this model can provide a solution for 26Al, 41Ca and 107Pd, with important contributions to 60Fe, which are inside the present uncertainty range of the 60Fe early solar system abundance. Such a model requires that 26Al is produced substantially on the AGB by cool bottom processing. The remaining inventory of short-lived species in the solar nebula would then be attributed to the continuous galactic processing, with the exception of 10Be, which must reflect production by later proton bombardment at a low level during early solar history.