Objectives: Selectively attending to a target talker while ignoring multiple interferers (competing talkers and background noise) is more difficult for hearing-impaired (HI) individuals compared to normal-hearing (NH) listeners. Such tasks also become more difficult as background noise levels increase. To overcome these difficulties, hearing aids (HAs) offer noise reduction (NR) schemes. The objective of this study was to investigate the effect of NR processing (inactive, where the NR feature was switched off, vs. active, where the NR feature was switched on) on the neural representation of speech envelopes across two different background noise levels [+3 dB signal-to-noise ratio (SNR) and +8 dB SNR] by using a stimulus reconstruction (SR) method. Design: To explore how NR processing supports the listeners’ selective auditory attention, we recruited 22 HI participants fitted with HAs. To investigate the interplay between NR schemes, background noise, and neural representation of the speech envelopes, we used electroencephalography (EEG). The participants were instructed to listen to a target talker in front while ignoring a competing talker in front in the presence of multi-talker background babble noise. Results: The results show that the neural representation of the attended speech envelope was enhanced by the active NR scheme for both background noise levels. The neural representation of the attended speech envelope at lower (+3 dB) SNR was shifted, approximately by 5 dB, toward the higher (+8 dB) SNR when the NR scheme was turned on. The neural representation of the ignored speech envelope was modulated by the NR scheme and was mostly enhanced in the conditions with more background noise. The neural representation of the background noise was modulated (i.e., reduced) by the NR scheme and was significantly reduced in the conditions with more background noise. The neural representation of the net sum of the ignored acoustic scene (ignored talker and background babble) was not modulated by the NR scheme but was significantly reduced in the conditions with a reduced level of background noise. Taken together, we showed that the active NR scheme enhanced the neural representation of both the attended and the ignored speakers and reduced the neural representation of background noise, while the net sum of the ignored acoustic scene was not enhanced. Conclusion: Altogether our results support the hypothesis that the NR schemes in HAs serve to enhance the neural representation of speech and reduce the neural representation of background noise during a selective attention task. We contend that these results provide a neural index that could be useful for assessing the effects of HAs on auditory and cognitive processing in HI populations.