We study the intensity spatial correlation function of optical speckle patterns above a disordered dielectric medium in the multiple scattering regime. The intensity distributions are recorded by scanning near-field optical microscopy (SNOM) with sub-wavelength spatial resolution at variable distances from the surface in a range which spans continuously from the near-field (distance ≪ λ) to the far-field regime (distance ≫ λ). The non-universal behavior at sub-wavelength distances reveals the connection between the near-field speckle pattern and the internal structure of the medium.