Electron spin resonance (ESR) of ${\mathrm{Gd}}^{3+}$ in the normal state $(T>{T}_{c})$ of ${R}_{1\ensuremath{-}x}{\mathrm{Gd}}_{x}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ $(R=\mathrm{Y},\mathrm{L}\mathrm{u})$ is reported. The results show that the exchange coupling between the rare-earth localized magnetic moment and the conduction electrons depends on the conduction electrons momentum transfer $(|{\mathbf{k}}_{F}^{\mathrm{in}}\ensuremath{-}{\mathbf{k}}_{F}^{\mathrm{out}}|=q)$, i.e., ${J}_{\mathrm{fs}}(q)$. The temperature dependence of the ESR linewidth yields a value for one of the exchange parameters, $〈{J}_{\mathrm{fs}}^{2}(q){〉}_{{E}_{F}}^{1/2}$, which is in agreement with that estimated from the slope of the initial linear decrease of ${T}_{c}$ by the ${\mathrm{Gd}}^{3+}$ impurities. These results indicate that the ${R}_{1\ensuremath{-}x}{\mathrm{Gd}}_{x}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ $(R=\mathrm{Y},\mathrm{L}\mathrm{u})$ compounds behave as conventional BCS superconductors, in agreement with previous reports.