Optical localization in strongly disordered photonic media is an attractive topic for proposing novel cavity-like structures. Light interference can produce random modes confined within small volumes, whose spatial distribution in the near-field is predicted to show hot spots at the nanoscale. However, these near-field speckles have not yet been experimentally investigated due to the lack of a high spatial resolution imaging techniques. Here, we study a system where the disorder is induced by random drilling air holes in a GaAs suspended membrane with internal InAs quantum dots. We perform deep-subwavelength near-field experiments in the telecom window to directly image the spatial distribution of the electric field intensity of disordered-induced localized optical modes. We retrieve the near-field speckle patterns that extend over few micrometers and show several single speckles of the order of λ/10 size. The results are compared with the numerical calculations and with the recent findings in the literature of disordered media. Notably, the hot spots of random modes are found in proximity of the air holes of the disordered system.