From numerical calculations based on Green's dyadic formalism. we show that a scanning near-field optical microscope (SNOM) working with a point-like illuminating probe delivers images that contain features directly related to the local density of photonic states (LDOS). More precisely, an unambiguous identification of the partial LDOSs (x, y or z polarized) can be made in the SNOM images when the solid angle of detection reaches 2 pi sr.