We have prepared polycrystalline R2NiMnO6 (R=Nd, Eu, Gd, Dy, and Y) samples by conventional solid-state reaction and all the samples have shown monoclinic structure with P2(1)/n space group. With the decrease in rare-earth ionic size (< r(R)>), the < Ni-O-Mn > bond angle decreases, correspondingly a decrease in ferromagnetic (FM) Curie temperature is noticed. In the dielectric measurement, the dielectric anomaly shifts to high temperature with the decrease in the < r(R)> and shows no correlation with the FM Curie temperature and hints the absence of apparent magnetodielectric (MD) coupling. Appearance of multiple relaxations in the dielectric study suggests the electrical heterogeneity of the system. The dielectric/impedance analysis has revealed a close correlation between dc conductivity and the dielectrics; in fact, both dc resistivity and the grain relaxations follow the variable range hopping mechanism. The thermal activation of charge carriers at the grain boundary led to Maxwell-Wagner interfacial polarization. Finally, dielectric study under magnetic field showed no effect, it implies that not only the intrinsic MD is absent, but also the extrinsic MD due to the lack of magnetoresistance.