Using a volume-limited sample of 550 groups from the Galaxy And Mass Assembly Galaxy Group Catalogue spanning the halo mass range 12.8 < log[Mh/M⊙] < 14.2, we investigate the merging potential of central Brightest Group Galaxies (BGGs). We use spectroscopically confirmed close-companion galaxies as an indication of the potential stellar mass buildup of low-redshift BGGs, z ≤ 0.2. We identify 17 close-companion galaxies with projected separations rp < 30 kpc, relative velocities Δv ≤ 300 km s-1, and stellar mass ratios MBGG/MCC ≤ 4 relative to the BGG. These close-companion galaxies yield a total pair fraction of 0.03 ± 0.01. Overall, we find that BGGs in our sample have the potential to grow in stellar mass due to mergers by 2.2 ± 1.5% Gyr-1. This is lower than the stellar mass growth predicted by current galaxy evolution models.