Experimental data on Li-ion transport have indicated that cation hopping, or ligand-exchange mechanism contribute considerably to the Li ion conduction in highly concentrated electrolyte regimes. In this work we performed molecular dynamics simulations of solutions of LiBF4 in sulfolane, up to [LiBF4] = 5.8 mol.L−1 (mole fraction of sulfolane = 0.57), to better understand the solution structure and the nature of the Li ion diffusion. The radial distribution functions, aggregation and connectivity analyses revealed that as the concentration of salt increases, the Li ions can be pictured as nodes of a network shared by BF4− and sulfolane molecules. The formation of these two different continuous networks sharing the cation seems to reach a sweet spot when the mole fraction of sulfolane is ca. 0.67, where the Li+ transference number achieves its maximum value in LiBF4–sulfolane mixtures. The autocorrelation functions of cation-anion and cation-sulfolane pair separations exhibit a non-exponential behaviour. Also, the relaxation dynamics of these solutions at and above room temperature recalls to the supercooled glass-forming liquids at temperatures near the glass transition. The relaxation process of the Li-anion pair is the major contributor to deviations from the Stokes-Einstein equation seen in the highly concentrated LiBF4–sulfolane solutions. These results showing the role played by the primary relaxation steps of Li ions in highly concentrated electrolytes can pave the way to innovative energy storage devices.