A critical issue in the asymptotic giant branch (AGB) self-enrichment scenario for the formation of multiple populations in globular clusters (GCs) is the inability to reproduce the magnesium isotopic ratios, despite the model in principle can account for the depletion of magnesium. In this work, we analyse how the uncertainties on the various p-capture cross sections affect the results related to the magnesium content of the ejecta of AGB stars. The observed distribution of the magnesium isotopes and of the overall Mg-Al trend in M13 and NGC 6752 are successfully reproduced when the proton-capture rate by 25Mg at the temperatures ˜100 MK, in particular the 25Mg(p, γ)26Alm channel, is enhanced by a factor ˜3 with respect to the most recent experimental determinations. This assumption also allows us to reproduce the full extent of the Mg spread and the Mg-Si anticorrelation observed in NGC 2419. The uncertainties in the rate of the 25Mg(p, γ)26Alm reaction at the temperatures of interest here leave space for our assumption and we suggest that new experimental measurements are needed to settle this problem. We also discuss the competitive model based on the supermassive star nucleosynthesis.