Satellite clock bias prediction plays a crucial role in enhancing the accuracy of satellite navigation systems. In this paper, we propose an approach utilizing Long Short-Term Memory (LSTM) networks to predict satellite clock bias. We gather data from the PRN 8 satellite of the Galileo and preprocess it to obtain a single difference sequence, crucial for normalizing the data. Normalization allows resampling of the data, ensuring that the predictions are equidistant and complete. Our methodology involves training the LSTM model on varying lengths of datasets, ranging from 7 days to 31 days. We employ a training set consisting of two days' worth of data in each case. Our LSTM model exhibits exceptional accuracy, with a Root Mean Square Error (RMSE) of 2.11 $\times$ 10$^{-11}$. Notably, our approach outperforms traditional methods used for similar time-series forecasting projects, being 170 times more accurate than RNN, 2.3 $\times$ 10$^7$ times more accurate than MLP, and 1.9 $\times$ 10$^4$ times more accurate than ARIMA. This study holds significant potential in enhancing the accuracy and efficiency of low-power receivers used in various devices, particularly those requiring power conservation. By providing more accurate predictions of satellite clock bias, the findings of this research can be integrated into the algorithms of such devices, enabling them to function with heightened precision while conserving power. Improved accuracy in clock bias predictions ensures that low-power receivers can maintain optimal performance levels, thereby enhancing the overall reliability and effectiveness of satellite navigation systems. Consequently, this advancement holds promise for a wide range of applications, including remote areas, IoT devices, wearable technology, and other devices where power efficiency and navigation accuracy are paramount.