Investigation of the coherence properties of a multimode semiconductor diode laser subjected to an external optical feedback is reported. Suitable multimode Lang-Kobayashi rate equations are solved numerically for this investigation. Suppression of threshold reduction has been found to occur for relatively long cavity delay times and for relatively high modal operation. This investigation provides numerical evidence of the role of multimode operation on the laser coherence without having to use any explicit decoherence element in the external cavity.