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Via molecular dynamics simulations of a generic glass former in the supercooled and normal liquid states, it is shown that spatial correlations of strain fluctuations exhibit a crossover from the well-established power-law  ~1/r^3-decay at long wavelengths to an exponential behavior, ~exp(-r/l_c) at intermediate distances. The characteristic length of the exponential decay grows both with temperature and time via,l_c \propto D(T)t , with D(T) being the temperature-dependent diffusion coefficient. This suggests that the crossover between the power-law and exponential decays is governed by a diffusion process.