The study presents an investigation of the optical properties of rectangular-shaped aluminum nanoantenna arrays formed on the surface of an emitting GeSiSn/Si heterostructure with multiple quantum wells. The positions of the localized surface plasmon resonance modes excited along the long (L) and short (S) sides of the examined nanoantennas are determined utilizing the technique of Fourier-transform infrared reflectance anisotropy spectroscopy. Experimental results demonstrate that both L- and S-modes are located in the near-infrared range, and as the lateral dimensions of the nanoantennas increase, the modes’ positions shift towards lower energies with an increase in the intensity of the resonance. The S-mode appears in the spectra as an overlay on the more pronounced L-mode with an intensity an order of magnitude lower. The geometry of the nanoantennas arrays with the resonance position near the photoluminescence peak of Ge0.84Si0.076Sn0.084/Si heterostructures (E ≈ 0.65 eV) is characterized.