Effect of electric field and ring dimension on the localization of direct and indirect exciton formed inside a CdTe/CdMnTe Concentric Double Quantum Ring (CDQR) has been studied using variational technique. The whole double ring structure is embedded inside a SiO2 matrix to enhance exciton localization. Electric field applied along the axial (z) axis tilts the band structure which promotes the carrier localization more in the edges than in the center of the ring. Thus, the stronger electric field gives a triangular confinement to the carrier in the edges which enhances the carrier stability. Along with the effect of electric field the ring dimension which determines the stability of the exciton retains has been estimated through the mean square distance. The effect of the location of the constituent carriers on the excitonic stability and the efficient carrier transfer from inner ring to outer ring has been calculated for both symmetric and asymmetric ring dimensions. Height of the ring has been varied to understand its effect on the localization of both direct and indirect exciton.