We report on the experimental investigation, by means of spatially-resolved cathodoluminescence spectroscopy, of rectangular all-dielectric Ge nanoantennas sustaining Fabry-Perot resonances. The combination of spatial and spectral resolution allows us to directly image the standing-wave pattern of the local density of optical states inside the nanoantennas, which is the fingerprint of the resonant Purcell contribution to the overall emission enhancement previously reported in the literature for the same structures. Our results confirm that the emission properties of Ge nanostructures can be effectively tuned by engineering the local density of optical states and that cathodoluminescence provides valuable information to experimentally address such modulation in their emission properties.