We study the relationship between velocity overshoot (VO) and quantum confinement (QC) in electron transport in Si nanosheet (NS) gate-all-around (GAA) fieldeffect transistors (FETs) through device simulation. VO is incorporated into the simulation with an energy transport (ET) model, and QC with a density-gradient (DG) model. We measure the effects of VO on the NS FETs by comparing their static characteristics obtained with the ET model and with a drift-diffusion (DD) model, which essentially cannot consider VO, and then examine the differences in the VO effects between the cases with and without QC. VO increases the drain current, and QC enhances this increase by gathering electrons inside the NS. This enhancement increases as the gate length decreases, although it eventually begins to decrease. It also generally increases as the gate voltage decreases. However, it shows a more complex behavior for a change in NS thickness, depending on the gate length and gate voltage. These behaviors of the VO effect enhancement by QC can be well explained from the effective potential acting on electrons in the NS.