This paper investigates several approaches for the short-term extrapolation of speech signals. The signal extrapolation methods are embedded into a nested two-stage spectral analysis-synthesis system for single-channel noise reduction in hearing aids. They predict additional signal samples in the low-frequency sub-bands of the first analysis stage and may compensate the additional algorithmic latency of the second, higher-resolution analysis stage in these bands. We thus achieve a higher spectral resolution in frequency bands below 3 kHz without increasing the algorithmic latency of the overall system. In the context of noise reduction, especially female voices benefit from the increased spectral resolution in the lower sub-bands of the first stage. We show that among the investigated approaches, both recursive neural-network-based extrapolation methods provide benefits in conjunction with a noise reduction algorithm and outperform our baseline linear extrapolation method.