We investigate the prospects for measuring the coherent elastic
neutrino-nucleus scattering of solar and supernova neutrinos in future NaI(Tl)
dark matter detection experiments. Considering the reduced background and
improved light yield of the recently developed NaI(Tl) crystals, more than
3σ observation sensitivities of the supernova neutrino within the Milky
Way are demonstrated. In the case of the solar neutrino, approximately 3
observations are marginal with a 1 ton NaI(Tl) experiment assuming an order of
magnitude reduced background, five photoelectron thresholds, and 5-year data
exposure