This paper describes a novel approach to improve monoaural speaker identification where two speakers are present in a single-microphone recording. The goal is to identify both of the underlying speakers in the given mixture. The proposed approach is composed of a double-talk detector (DTD) as a pre- processor and speaker identification back-end. We demonstrate that including the double-talk detector improves the speaker identification accuracy. Experiments on GRID corpus show that including the DTD improves average recognition accuracy from 96.53% to 97.43%.