Starting from tri-bimaximal mixing at high scale, we investigate if it is possible to generate a sizable value of |Ue3|, while at the same time keeping solar neutrino mixing near its measured value, which is close to sin2 θ12 = 1/3 through renormalization group corrections. Generation of indicated values of |Ue3| ≈ 0.1 via this effect requires the neutrinos to be quasi-degenerate in mass. If we consider Standard Model (SM) as the low energy effective theory then the required value of the mass scale is beyond 2.3 eV which is the current constraint from tritium β-decay. On the other hand considering the Minimal Supersymmetric Standard Model (MSSM) as the effecitve theory at low energy it is possible to generate the non-zero Ue3 values hinted by the current global analysis for lower m0 values. The consistency with the allowed range of sin2 θ12 together with large running of |Ue3| forces one of the Majorana phases to be close to π This implies large cancellations in the effective Majorana mass governing neutrino-less double beta ((ββ)0ν−)decay, constraining it to lie near its minimum allowed value of m0 cos 2θ12, where m0 ≳ 0.1 eV.