A systematic X-ray absorption spectroscopy investigation of the local coordination in gallium nanostructures has been performed as a function of temperature and particle size. It is shown that the nanostructure strongly affects the polymorphism of solid gallium and the (meta)stability range of the liquid phase (in agreement with previous works) and that the surface tension acts in the same direction as hydrostatic pressure in stabilizing the Ga solid phases. The effect of surface free energy is first to favor the metallic arrangement of the delta phase and then to stabilize a liquid-like phase based on dimeric molecules even at 90 K. The Ga-Ga distance in the dimers is lower in the liquid phase than in the alpha solid. The experimental results are discussed in comparison with molecular dynamic calculations to assess the presence of covalent character of the dimeric Ga-2 units in liquid nanostructured gallium.