Short gamma-ray bursts (SGRBs) are widely believed to be from mergers of binary compact objects involving at least one neutron star and hence have a broad range of spatial offsets from their host galaxies. In this work, we search for possible correlations between the emission properties of 18 SGRBs and their offsets from the host galaxies. The SGRBs with and without extended emission do not show significant differences between their offset distributions, in agreement with some previous works. There are, however, possible correlations between the optical and X-ray afterglow emission and the offsets. The underlying physical origins are examined.