A linear-response formulation of the dc spin pumping, i.e., a spin injection from a precessing ferromagnet into an adjacent spin sink, is developed in view of describing many-body effects caused by spin fluctuations in the spin sink. It is shown that, when an itinerant ferromagnet near Tc is used as the spin sink, the spin pumping is largely increased owing to the fluctuation enhancement of the spin conductance across the precessing ferromagnet/spin sink interface. As an example, the enhanced spin pumping from permalloy into nickel palladium alloy (Tc ~ 20K) is analyzed by means of a self-consistent renormalization scheme, and it is predicted that the enhancement can be as large as tenfold. ; Comment: 11pages, 7figures