In recent years a number of observers ( Hutching et al. 1984, Astrophys.J.Suppl. 55, 319; Wyckoff et al. 1981, Astrophys.J. 247, 750; Gehren et al. 1984, Astrophys.J. 278, 11; Malkan et al. 1984 Astrophys.J. 280, 66; Malkan 1984, Astrophys.J. 287, 555) have carried out high-sensitivity imaging studies of quasars. Most of the objects selected were such that their apparent 'redshifts' were less than 0.7. In most of these cases a nebulosity has been found around the quasar. Assuming the cosmological hypothesis, these investigators have interpreted the nebulosity as starlight from the underlying galaxy in which the quasar nucleus resides. On the other hand, the author has proposed a theory of quasars according to which the quasars are stars which are undergoing high-speed mass loss and have no redshifts. (Varshni, 1974a, 1974b, 1975, 1977, 1985). According to our theory we interpret the nebulosity as an envelope of ionized and neutral gases which have been ejected from the quasar. Some dust may also be present. We further predict that similar nebulosity should occur around some of the Wolf-Rayet stars, planetary nuclei (which have WR type of spectra) and Be stars. We request that observations be carried out to test this prediction. The detection of nebulosity depends on the plate scale, limiting magnitude, and quality of the observations. Clearly these should be similar to those in the quasar studies. A good sample size would be desirable. The stars should not be in a crowded or obscured field.