Monaural speech enhancement has achieved remarkable progress recently. However, its performance has been constrained by the limited spatial cues available at a single microphone. To overcome this limitation, we introduce a strategy to map monaural speech into a fixed simulation space for better differentiation between target speech and noise. Concretely, we propose SE-TerrNet, a novel monaural speech enhancement model featuring a virtual binaural speech mapping network via a two-stage multi-task learning framework. In the first stage, monaural noisy input is projected into a virtual space using supervised speech mapping blocks, creating binaural representations. These blocks synthesize binaural noisy speech from monaural input via an ideal binaural room impulse response. The synthesized output assigns speech and noise sources to fixed directions within the perceptual space. In the second stage, the obtained binaural features from the first stage are aggregated. This aggregation aims to decrease pattern discrepancies between the mapped binaural and original monaural features, achieved by implementing an intermediate fusion module. Furthermore, this stage incorporates the utilization of cross-attention to capture the injected virtual spatial information to improve the extraction of the target speech. Empirical studies highlight the effectiveness of virtual spatial cues in enhancing monaural speech enhancement. As a result, the proposed SE-TerrNet significantly surpasses the recent monaural speech enhancement methods in terms of both speech quality and intelligibility.