Plasmonic antennas channel incoming light into a confined near field that comes along with strong field gradients at the edges. Transverse field gradients are capable of driving quadrupole transitions in a more effective way than the weak longitudinal field gradient in dipolar light. Cuprous oxide Rydberg excitons with principal quantum number $n$ between 5 and 15 are several tens to a few hundreds of nanometers in diameter and can have different orbital angular momentum quantum numbers. Usually, only $P$- and $F$-excitons are electric dipole allowed, while $S$- and $D$-excitons remain dark. Here, we use 30-nm-wide and 60- to 110-nm-long plasmonic aluminum nanoantennas deposited on the cuprous oxide crystal surface to create transverse field gradients in similar spatial dimensions as the size of the Rydberg excitons. This way, light field and matter wave function overlap spatially and quadrupole transitions of $S$excitons are enhanced. The relative enhancement of the $S$-exciton oscillator strength with respect to the $P$-exciton oscillator accounts for a factor of up to 1.4.