The disclosure relates to a turbofan nacelle including a thrust reverser, the thrust reverser including a movable cover moving back from a closed position in which the thrust is not reversed to an open position for uncovering cascades that reverse the direction of the flow of cold air which is diverted from the annular stream of secondary air, the movable cover including a radially outer portion intended for being adjacent to a leading edge of a wing of an aircraft. The movable cover includes on the radially outer portion at least one cut-out intended for avoiding interference with a movable slat of the leading edge of the wing of the aircraft, as well as a panel for closing the cut-out, the closing panel including a stationary portion at least partially covered by an upstream portion of the movable cover when the movable cover is in the open position.