In several extensions of the Standard Model of Particle Physics (SMPP), the neutrinos acquire electromagnetic properties such as the electric millicharge. Theoretical and experimental bounds have been reported in the literature for this parameter. In this work, we first carried out a statistical analysis by using data from reactor neutrino experiments, which include elastic neutrino-electron scattering (ENES) processes, in order to obtain both individual and combined limits on the neutrino electric millicharge (NEM). Then we performed a similar calculation to show a estimate of the sensitivity of future experiments of reactor neutrinos to the NEM, by involving coherent elastic neutrino-nucleus scattering (CENNS). In the first case, the constraints achieved from the combination of several experiments are $-1.1\times 10^{-12}e < q_{\nu} < 9.3\times 10^{-13}e$ ($90\%$ C.L.), and in the second scenario we obtained the bounds $-1.8\times 10^{-14}e < q_{\nu} < 1.8\times 10^{-14}e$ ($90\%$ C.L.). As we will show here, these combined analyses of different experimental data can lead to stronger constraints than those based on individual analysis. Where CENNS interactions would stand out as an important alternative to improve the current limits on NEM.