Quasi-elastic neutron scattering (QENS) and pulsed-field-gradient nuclear magnetic resonance (PFGNMR) analyses of a nanofluid composed of silicon dioxide (SiO2) nanoparticles (sized 100, 300, or 500 nm) and a base fluid of ethylene glycol aqueous solution were performed. The aim was to elucidate the mechanism increase in the thermal conductivity of the nanofluid above its theoretical value. Typically, the self-diffusion coefficient of liquid molecules in nanofluids can indicate the effect of the nanoparticles on thermal transport in nanofluids as well as the molecular dynamics of the liquid surrounding the nanoparticles. At 298 and 333 K, the obtained experimental results indicate that SiO2 particles may decrease the self-diffusion coefficient of the liquid molecules in the ethylene glycol aqueous solution because of their highly restricted motion around these nanoparticles. The self-diffusion coefficient of the liquid molecules comprising 300 nm-sized particles is lower than that of the nanofluids comprising 100 and 500 nm-sized particles. At a constant temperature, the thermal conductivity increases as the self-diffusion coefficient of the liquid molecules decreases in the SiO2 nanofluids.