With the Infrared Space Observatory, we conducted 3 x 3 pixel imaging photometry of 12 luminosity class III stars, which were previously presumed to have dust particles around them, at far-infrared wavelengths (60 and 90 mum). Eleven out of 12 targets show a peak of excess (above photosphere) far-infrared emission at the location of the star, implying that the dust particles are truly associated with stars. To estimate the size of the excess emission source, the flux ratio of center to boundary pixels of the 3 x 3 array was examined. The radius of the dust emission is found to be similar to 3000 to similar to 10,000 AU for a thin shell distribution and similar to 5000 to similar to 25,000 AU for a uniform distribution. We consider three models for the origin of the dust: disintegration of comets, sporadic dust ejection from the star, and emission from nearby interstellar cirrus. The data seem to rule out the first model (as far as the "Kuiper belt-like" particles are assumed to be large blackbody grains) but do not enable us to choose between the other two models.