Egocentric gaze prediction serves as a critical indicator for decoding human visual attention and cognitive processes, but its inherently limited field of view creates prediction challenges. Although exo-view data provides supplementary contextual information, it exhibits significant spatial and semantic gaps. Existing methods focus solely on isolated feature encoding in single-view paradigms, neglecting cross-view gaze correlations. To make up for this gap, we make the first exploration of cross-view gaze relationship for egocentric gaze prediction, and propose Ego-PMOVE, a novel Prompt-aware Mixture of View Experts network. Unlike prior cross-view studies that forcibly align cross-view features thereby introducing inference noise, we leverage the popular Mixture-of-Experts (MoE) and a set of flexible prompts to disentangle features from different views into three parallel experts: a view-shared expert directly modeling common semantic relationships, a view-discrepancy expert adaptively adjusting the spatial position, scale and shifts based on different view-specific features, and an egocentric expert extracting independent features to compensate for the case of missing exocentric data. To balance these experts, we further design a soft router to dynamically weight them for mining useful information while suppressing noise. A view-query gaze decoder then generates view-specific gaze attention maps, jointly optimized by gaze-heamap and cross-view contrastive loss that regularize both shared and divergent features for accurate gaze prediction. Extensive experiments across the multi-view EgoMe dataset and single-view Ego4D and EGTEA Gaze++ datasets demonstrate the effectiveness and generalizability of our approach. Our code will be released soon.