Type Ia supernovae (SNe Ia) are thermonuclear explosions of carbon-oxygen white dwarfs (WDs) that accrete mass from a binary companion, which can be either a non-degenerate star (a main-sequence star or a giant) or an other WD in a binary merger (single- and double-degenerate scenario, respectively). In population-synthesis studies of SNe Ia the contribution of asymptotic giant branch (AGB) stars to either scenario is marginal. However, most of these studies adopt simplified assumptions to compute the effects of wind mass loss and accretion in binary systems. This work investigates the impact of wind mass transfer on a population of binary stars and discusses the role of AGB stars as progenitors of SNe Ia.