Sterile massive neutrinos are a natural extension of the standard model of elementary particles. The energy density of the extra sterile massive states affects cosmological measurements in an analogous way to that of active neutrino species. We perform here an analysis of current cosmological data and derive bounds on the masses of the active and the sterile neutrino states, as well as on the number of sterile states. The so-called (3 + 2) models, with three sub-eV active massive neutrinos plus two sub-eV massive sterile species, is well within the 95% CL allowed regions when considering cosmological data only. If the two extra sterile states have thermal abundances at decoupling, big bang nucleosynthesis bounds compromise the viability of (3 + 2) models. Forecasts from future cosmological data on the active and sterile neutrino parameters are also presented. Independent measurements of the neutrino mass from tritium beta-decay experiments and of the Hubble constant could shed light on sub-eV massive sterile neutrino scenarios.