Graph neural networks (GNNs) have received remarkable success in link prediction (GNNLP) tasks. Existing efforts first predefine the subgraph for the whole dataset and then apply GNNs to encode edge representations by leveraging the neighborhood structure induced by the fixed subgraph. The prominence of GNNLP methods significantly relies on the adhoc subgraph. Since node connectivity in real-world graphs is complex, one shared subgraph is limited for all edges. Thus, the choices of subgraphs should be personalized to different edges. However, performing personalized subgraph selection is nontrivial since the potential selection space grows exponentially to the scale of edges. Besides, the inference edges are not available during training in link prediction scenarios, so the selection process needs to be inductive. To bridge the gap, we introduce a Personalized Subgraph Selector (PS2) as a plug-and-play framework to automatically, personally, and inductively identify optimal subgraphs for different edges when performing GNNLP. PS2 is instantiated as a bi-level optimization problem that can be efficiently solved differently. Coupling GNNLP models with PS2, we suggest a brand-new angle towards GNNLP training: by first identifying the optimal subgraphs for edges; and then focusing on training the inference model by using the sampled subgraphs. Comprehensive experiments endorse the effectiveness of our proposed method across various GNNLP backbones (GCN, GraphSage, NGCF, LightGCN, and SEAL) and diverse benchmarks (Planetoid, OGB, and Recommendation datasets). Our code is publicly available at \url{https://github.com/qiaoyu-tan/PS2}
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